People waited after receiving the COVID-19 vaccine at the East Boston Neighborhood Health Center clinic in Revere.Erin Clark/Globe Staff Thousands of people in Massachusetts are receiving COVID-19 shots each day, leaving many to wonder what to expect and how to care for themselves right after theyâve been vaccinated. Massachusetts residents 16 and older are now eligible to book appointments, and so far more than 5 million COVID-19 shots have been administered in the state, with more than 2 million people fully vaccinated against the virus. Some people may experience side effects after getting a COVID-19 vaccine, according to the Centers for Disease Control and Prevention.