Allergic reactions reported in two health workers who received a dose of Pfizer’s vaccine in Alaska this week have reignited concerns that people with a history of extreme immune flare-ups might not be good candidates for the newly cleared shots.

The two incidents follow another pair of cases in Britain. Three of the four were severe enough to qualify as anaphylaxis, a severe and potentially life-threatening reaction. But all four people appear to have recovered.

Health officials on both sides of the pond are vigilantly monitoring vaccinated people to see if more cases emerge. Last week, British drug regulators recommended against the use of Pfizer’s vaccine in people who have previously had anaphylactic reactions to food, medicines or vaccines.

And on Thursday, Dr. Doran Fink, deputy director of the Food and Drug Administration’s clinical division of vaccines and related products applications, addressed the issue during a meeting about the vaccine made by Moderna that contains similar ingredients and is expected to soon receive emergency use authorization, or E.U.A., from the agency.

“We anticipate that there may be additional reports, which we will rapidly investigate,” Dr. Fink said, adding that robust surveillance systems were in place to detect these rare events.

Still, Dr. Fink said that “the totality of data at this time continue to support vaccinations under the Pfizer E.U.A., without new restrictions.”

The F.D.A., he added, would work with Pfizer to revise fact sheets and prescribing information for the vaccine so that the public would understand the risk of allergic reactions and know how to report them.

What do we know about the people who had bad reactions?

The first two confirmed cases of allergic reactions came from two health care workers in Britain. Both had a medical history of serious allergic reactions, but had not previously been known to have trouble with any of the vaccine’s ingredients. After an injection of epinephrine — the typical treatment for anaphylaxis — both recovered.

(A third British incident described as a “possible allergic reaction” was also reported and appears to have been minor.)

On Wednesday, two health workers in Alaska experienced reactions as well. One was too mild to be deemed anaphylaxis. But the other, which occurred in a middle-aged woman with no history of allergies, was serious enough to warrant hospitalization, even after she got a shot of epinephrine.

“What is happening does seem really unusual to me,” said Dr. Kimberly Blumenthal, an allergist, immunologist and drug allergy researcher at Massachusetts General Hospital. Vaccine-related allergic reactions are typically rare, occurring at a rate of about one in a million.

Dr. Blumenthal also pointed out that it was a bit bizarre to see allergic reactions clustering in just two locations: Britain and Alaska. Zeroing in on the commonalities between the two hot spots, she said, might help researchers puzzle out the source of the problem.

Do we know for sure that their reactions were caused by the vaccine?

British and U.S. agencies are investigating the causes, but no official has declared a direct link.

But Dr. Blumenthal suspects they were connected to the shots, because the reactions were immediate, occurring within minutes of injection.

“We have to think it was related because of the timing,” she said.

Nor is it known if a particular ingredient might have been the cause. Pfizer’s vaccine contains just 10 ingredients. The most important is a molecule called messenger RNA, or mRNA — genetic material that can instruct human cells to make a coronavirus protein called spike. Once manufactured, spike teaches the immune system to recognize the coronavirus so it can be fought off in the future. Messenger RNA, which is naturally found in human cells, is unlikely to pose a threat, and degrades within about a day of being injected.

The other nine ingredients are a mix of salts, fatty substances and sugars that stabilize the vaccine. None are common allergens. The only chemical with a history of causing allergic reactions is polyethylene glycol, or PEG, which helps package the mRNA into an oily sheath, protecting it as it goes into human cells.

But PEG is, generally speaking, inert and widespread. It’s found in ultrasound gel, laxatives like Miralax and injectable steroids, among other drugs and products, Dr. Blumenthal said. Despite the chemical’s ubiquity, she said, “I’ve only seen one case of a PEG allergy — it’s really, really uncommon.”

It’s still possible that something else could be causing the reactions — perhaps a factor related to how the vaccines are transported, thawed or administered, Dr. Blumenthal said.

Did the volunteers in Pfizer’s clinical trials have any bad reactions?

A small number of volunteers in Pfizer’s clinical trials experienced allergic reactions. Just one of the 18,801 participants who received the vaccine in a late-stage trial had anaphylaxis, and the incident was deemed unrelated to the vaccine, said Steven Danehy, a spokesman for Pfizer. No severe reactions were found in people who got a placebo shot.

Pfizer excluded people with a history of anaphylaxis to vaccines from its clinical trials.

What does the F.D.A. say about these reactions?

Several experts raised concerns about the allergic reactions in meetings convened to discuss both Pfizer’s and Moderna’s vaccines. The agency has advised caution, noting that health care providers should not administer the vaccine to anyone with a “known history of a severe allergic reaction” to any component of the vaccine — a standard warning for vaccines.

Should people with mild allergies wait to get vaccinated?

There’s no evidence that people with mild allergies, which are quite common, need to avoid the vaccine. Allergies are, simply put, the product of an inappropriate immune response against something harmless — pollen, peanuts, cat dander and the like. In many cases, the results of this overreaction are mild symptoms such as a runny nose, coughing or sneezing.

But allergies are specific: A reaction to one substance does not guarantee a reaction to another. On Monday, the American College of Allergy, Asthma and Immunology released guidance stating that people with common allergies “are no more likely than the general public to have an allergic reaction to the Pfizer-BioNTech Covid-19 vaccine.”

William Amarquaye, a clinical pharmacist at Brandon Regional Hospital, said he wouldn’t let his asthma or allergies stop him from taking the vaccine when it is offered to him in the next few weeks. He’s also never had trouble with other vaccines he has taken in the past.

“It should still be OK to take the vaccine,” Dr. Amarquaye said. “I’m actually excited about it.”

What about people with a history of severe allergies?

Most people in this category should be good to go, too, said Dr. Eun-Hyung Lee, an expert in allergy and immunology at Emory University.

Guidelines released by the Centers for Disease Control and Prevention identify only one group of people who might not want to get Pfizer’s vaccine: those with a known history of severe allergic reactions to an ingredient in the injection.

People with a history of anaphylaxis to any other substance, including other vaccines or injectable drugs, can still get the vaccine, but should consult their health care providers and be monitored for 30 minutes after getting their shots. Everyone else, like people with mild or no allergies, need to wait only 15 minutes before leaving the vaccination site.

“In general, the immediate reactions that require epinephrine are those that happen within the first 30 minutes,” said Dr. Merin Kuruvilla, an allergist and immunologist at Emory University.

Some people will understandably be concerned. Dr. Taison Bell, a critical care physician at UVA Health in Charlottesville, Va., said he worried about his 7-year-old son, Alain, who is severely allergic to several foods, including wheat, peanuts and cow’s milk. Alain has about two bouts of anaphylaxis each year.

It’s a bit of a relief that Alain is “later in the prioritization schema,” Dr. Bell said. By the time a vaccine is ready for him, he said, “we’ll get a better sense for how serious this is.” The family plans to discuss their situation with Alain’s doctor.

Ultimately, it’s unlikely that any of the ingredients in a coronavirus vaccine would cause Alain any issues. Alain has tolerated other vaccines, including the flu shot, in previous years, and is looking forward to his own shot at immunization to the coronavirus, said Dr. Bell, who received his first dose of Pfizer’s vaccine on Tuesday.

What about Moderna’s vaccine?

Two volunteers in Moderna’s late-stage clinical trial developed anaphylactic reactions, the company reported at the F.D.A. committee meeting on Thursday. Neither was deemed to be linked to the company’s vaccine, which also contains mRNA, because they occurred weeks or months after the participants received their shots. One of these volunteers also had a history of asthma and a shellfish allergy.

Moderna, unlike Pfizer, did not exclude people with a history of anaphylaxis from its trials.

Dr. Tal Zaks, the company’s chief medical officer, said that while Moderna’s vaccine recipe was similar to Pfizer’s, key molecular differences existed that could set the two products on different paths. He said that bad reactions to Pfizer’s vaccine did not guarantee that similar events would happen in relation to the Moderna shots.

Both vaccines do, however, include a version of PEG.

Dr. Blumenthal and others said that anyone concerned about having an allergic reaction to a vaccine should seek the advice of a health care provider.

For anyone getting the vaccine, it’s all about “balancing out the risks,” Dr. Lee, of Emory, said. Allergic reactions can be dangerous. But they are rare and treatable, and the tools to combat them should be available at all vaccination sites. The coronavirus, on the other hand, can have far graver consequences.

“When it’s my turn in line, I think weighing these odds is what I would do,” Dr. Lee said.