Could I get pregnant if I had unprotected sex three days before my period?

Possibly. You can only get pregnant when you are ovulating, which is normally in the middle of your cycle (usually day 14 of a 28 day cycle). However, some people ovulate at different times. Men's sperm can remain active for up to 2-3 days. With so many variations and irregularities, it is safe to assume that you could get pregnant anytime you have unprotected intercourse.
Possibly. It is possible to get pregnant at any time. If you don't want to get pregnant, you should always use birth control.