Is it possible to get pregnant a few days before your period and still have a period? because my last period was normal after having unprotected sex

Possible pregnancy: If you had a period which was "normal " in terms of when it occurred, and the length (just minor spotting or a short one day flow may not be a real "period") pregnancy occurring at the time of ovulation will prevent a "real" period, but implantation bleeding may present as a "period" and be coexistent with early pregnancy. Get a serum HCG test to be sure.

Low risk: Just prior to your period is not the highest-risk time of the month for getting pregnant. Physiologically, you can't have a period if you are pregnant. So if you had a normal period you aren't pregnant. It can be tricky because occasionally there is bleeding in early pregnancy that makes you think you had period when you didn't. Do a pregnancy test if you are worried.