Is it possible that i could get pregnant?

I'm 22 years old and happily married, we weren't planning on having a baby for another few years but last night during sex he c*m inside. We don't use condoms because I'm allergic to latex and the sheep skin condoms. I don't take birth control because I work and don't have time to go to the doctor to get them. I've never been concerned because we have been sexually active for 5 years and never had a scare before. The thing is, I'm due for my period on the 6th, is it possible I could still conseve despite how close my period is? Help please?