Yes. The U.S. vaccine safety system ensures that safety is the top priority when creating vaccines. There have been thousands of clinical trial participants for the vaccine, and if the FDA determines that the vaccines are safe and effective, they are approved for emergency use. The FDA gave full approval for the Pfizer-BioNTech COVID-19 Vaccine (aka Comirnaty) on August 23, 2021, for the prevention of COVID-19 disease in individuals 16 years of age and older.
Vaccine-safety monitoring systems continuously monitor for any adverse reactions that had not occurred during the clinical trials.
Additionally, smartphone technology allows for easy access to surveys where patients monitor how they are feeling and any side effects they may have after the vaccine, via the "V-Safe" app. The app also provides second dose alert reminders when necessary.