British health officials have warned that people with a history of "significant" allergic reactions to vaccines, medicine or food should not be given Pfizer's COVID-19 vaccine. Two people in the first U.K. COVID-19 vaccine group, both health care workers, experienced "adverse reactions" after taking it. So far, only three cases of allergic reactions have been reported in the United States. A pair of health care workers at a hospital in Alaska experienced allergic reactions after taking the vaccine. One worker, who had no previous history of allergies, had a serious reaction, known as anaphylaxis, while the second suffered a less-serious allergic reaction. A second serious reaction was reported at a separate hospital in Alaska later this week. All three were treated and swiftly recovered. The Centers for Disease and Control and Prevention recommends that people with a "history of severe allergic reaction such as anaphylaxis to any vaccine or to any injectable therapy" should take "precaution," but do not need to avoid the vaccine altogether. That guidance is based off Pfizer's clinical trials, in which about 22,000 people received the vaccine and well under 1% had possible allergic reactions to it. "Among a subset of participants in the phase 2/3 clinical trials, 0.63% of participants in the vaccinated group had hypersensitivity-related adverse events, possibly representing allergic reactions (compared to 0.51% in the placebo group)," reads the CDC's Interim Clinical Considerations for use of the Pfizer vaccine. During the trials, "there were no anaphylaxis cases," Pfizer said. "Overall, there were no safety signals of concern identified in our clinical trials, including no signal of serious allergic reactions associated with vaccine," a Pfizer spokesperson told CBS News. "However, reports of adverse events outside of clinical studies are a very important component to our pharmacovigilance activities and we will review all available information on this case and all reports of adverse events following vaccination." "We don't yet have all the details of the report from Alaska about a potential serious allergic reaction but are actively working with local health authorities to assess," said the spokesperson. "We will closely monitor all reports suggestive of serious allergic reactions following vaccination and update labeling language if needed." People who wanted to participate in Pfizer's Phase 3 trial "were excluded if they had a history of severe adverse reaction associated with a vaccine and/or severe allergic reaction (e.g., anaphylaxis) to any component of the investigational vaccine," according to the company. So it's true that people with a history of severe allergic reactions are going to be taking the vaccine for the first time as it is released to the public. Dr. Mark Dykewicz, an allergy and immunology expert at St. Louis University Hospital and a member of the Food and Drug Administration's Allergenic Products Advisory Committee, said he's been fielding questions about the vaccine from patients with an anaphylactic history. "I'm telling my patients that they should go ahead and get it," he said. According to Dykewicz, the risk is lessened by the presence of medical personnel at the time of injection, when a reaction is most common. CDC guidance calls for vaccine providers to observe "patients with a history of anaphylaxis (due to any cause) for 30 minutes after vaccination... to monitor for the occurrence of immediate adverse reactions," and for "all other persons" to be observed "for 15 minutes after vaccination." Dykewicz stressed that the benefit of protecting against COVID-19 outweighs the risk of a one-in-a-million chance of severe allergic reaction to a vaccine. "In balancing the pros and cons of this I would recommend that they get it," he said. "Overall, the general risk of anaphylaxis to vaccines (of all types), is about 1 [in] 1,000,000," according to Dr. David Peden, a pediatric allergy and immunology expert at the University of North Carolina at Chapel Hill Medical School and chair of the allergenic products advisory committee. "It does happen, but is extremely rare," he said. Since allergic reactions to Pfizer's vaccine have yet to be formally studied, it is not yet known what component, or components, of the drug can cause a reaction. "It is unclear which element of the vaccine is responsible for the tiny number of allergic emergencies associated with the vaccine," Peden said. According to Dykewicz, the Pfizer vaccine doesn't contain any of the "usual suspects," like gelatin, that have been known to cause a reaction. The part of a vaccine that attacks a virus — messenger RNA, in the case of Pfizer and Moderna — is only one component; they also contain small amounts of other ingredients, known as excipients. "Stabilizers," commonly sugars or gelatin, are excipients that help keep the vaccine potent during transportation and storage, according to the CDC. Pfizer's vaccine, which is kept at 94 degrees below zero Fahrenheit to maintain efficacy, does not contain gelatin. It is also preservative-free. "Most allergy/immunology physicians worry most about the additives to stabilize the vaccine, rather than the actual vaccine antigen," Peden said. It's too early to know if any similar cases may arise with Moderna's vaccine, which the FDA authorized on Friday. A representative for Moderna told members of the FDA's vaccine advisory panel that there was one report of anaphylaxis during trials, but it came more than two months after vaccination and was therefore likely not linked to the vaccine, STAT reports. Moderna's chief medical officer also noted during the meeting that the vaccine's lipid nanoparticles — tiny spheres of fatty material used to deliver the mRNA — used in its vaccine are not the same lipid nanoparticles as Pfizer's. Dykewicz, however, said that without knowing which component of Pfizer's vaccine caused the reactions, it is impossible to know if Moderna's vaccine has it in common. "The bottom line is at this point we don't know what the component or components that's leading to an allergic reaction," he said. Zeroing in on the culprit will take time, time that will also help determine how common such reactions are in the general population. Dr. Amal Assa'ad, associate director of the Division of Allergy and Immunology at Cincinnati Children's Hospital and a member of the advisory committee, said that without a "denominator" it will be hard to tell if allergic reactions are happening at the anticipated rate. And people who have never had allergic reactions may still be at risk for one with any new substance, including vaccines. Still, experts stress that the risk is very small, and even those who have a history of allergic reactions should be immunized. "The risk, while not zero, is extremely small, and people without any vaccine anaphylaxis history should not avoid vaccination on this basis," Peden said. "... In general, even with a history of allergy (except for a specific history to anaphylactic reaction to another vaccine), people should proceed with COVID-19 immunization, especially if they are in a high risk group."