Can you get pregnant if you had sex a day after your period finished?

You can pregnant at any point of the month its just a lot higher a chance when you are ovulating.
If you have unprotected sex then you run the risk of becoming pregnant.

Anytime you have sex you run the risk of pregnancy, birth control or not. Birth control is not 100% effective, and I don't know if you are using it or not.

With that said, yes it is possible, but highly unlikely, since you do not ovulate for about 12 - 14 days after the first day of your period. It all depends on your cycle.