Is the COVID-19 vaccine safe?

Yes. The vaccine went through a rigorous testing process, which included a clinical trial with 30,000 people. The most adverse reactions were two test subjects reporting an allergic reaction after receiving the vaccine in the UK. The Centers for Disease Control and Prevention (CDC) says it is still safe for people with allergy problems, and those who have experienced severe reactions to prior vaccines or injectable drugs can still get the Pfizer/BioNTech vaccine, but should discuss the risks with their doctors and be monitored for 30 minutes afterward.

Sources and more information:

https://www.cdc.gov/coronavirus/2019-ncov/vaccines/safety.html

https://www.pbs.org/newshour/health/cdc-says-people-with-history-of-severe-allergic-reactions-can-get-covid-19-vaccine

https://www.foxnews.com/politics/pence-gets-coronavirus-vaccine