Yes, people who have had severe allergic reactions or who have had any type of immediate allergic reaction to a vaccine or injectable therapy are advised to take the COVID-19 vaccine. They should be monitored for at least 30 minutes after getting the vaccine (whereas all others are monitored for 15 minutes post-vaccination. It is still recommended that you take the COVID-19 vaccination unless one of those allergic items is contained within the vaccine.
All vaccination providers should have appropriate personnel, mediation, and equipment to handle an allergic reaction.
You should not get the second dose of COVID-19 mRNA vaccine if you either had a severe allergic reaction after getting the first dose, or had an immediate reaction (within 4 hours) of getting the first dose, such as hives, swelling, and wheezing (respiratory distress).
(‘Reported side effects’ and ‘serious side effects’ are defined in previous questions.)
If you only experience a red, itchy, swollen, or painful rash where the first injection occurred, you should STILL get the second dose. The rash is referred to as “COVID arm.” Treat the symptom you have with appropriate medication (antihistamine, pain reliever). It may be recommended that you receive the second dose in the opposite arm, but having this rash is NO indication that you will have a severe allergic reaction after the second dose, or even that the rash will recur.