I have had irregular periods so the doctors prescribed birth control pills, I'm on week two and I had unprotected sex about two hours after I take the pill. My period started the next day and I just wanted to know if that could mean I'm pregnant?

Generally it takes about a month for birth controls pills to have an effect on your period. But ANY time there is penile insertion there is the risk of pregnancy. You can reduce the risk, but not eliminate it. So it is possible, though unlikely.

Being prescribed birth control to regulate a period is not an excuse to become sexually active.