Are you allowed to drive home on your own after getting the covid-19 vaccine?

I drove there and back for both of my vaccines. Unless you have a severe reaction, it will not be a problem. Everyone was driving there. Hopefully, you won't even know you had the vaccine. But, rest if it bothers you.

Only after 15 minutes in the post shot waiting room. 

There’s a possibility that you can have an adverse reaction to the vaccine so you’re told to wait at the site for at least 15 minutes before you can go home. 

Why wouldn’t you be allowed to drive home. It’ll take several hours before the symptoms kick in. If it’s your first shot, you’ll most likely have mild symptoms, nothing that will prevent you from doing ordinary things.