(Info from the CDC – https://www.cdc.gov/coronavirus/2019-ncov/vaccines/faq.html)
All the COVID-19 vaccines being used have gone through rigorous studies to ensure they are as safe as possible. Systems that allow CDC to watch for safety issues are in place across the entire country.
The U.S. Food and Drug Administration (FDA) has granted Emergency Use Authorizations for COVID-19 vaccines that have been shown to meet rigorous safety criteria and be effective as determined by data from the manufacturers and findings from large clinical trials. Watch a video describing the emergency use authorization. Clinical trials for all vaccines must first show they meet rigorous criteria for safety and effectiveness before any vaccine, including COVID-19 vaccines, can be authorized or approved for use. The known and potential benefits of a COVID-19 vaccine must outweigh the known and potential risks of the vaccine.