Does Missing A Dose Of Birth Control Pills Increase Chance Of Pregnancy?

I missed the first day of my new pack of birth control pills. However, I took it the next day at three pm and then took it again at my normal time of nine pm. This made me sick, and I threw up that night starting at about one am, and I threw up a lot. I then took my birth control at the regular time the next day, and the following day had unprotected sex. He didn't *** a lot inside of me, he started and then pulled out halfway through. I can't decide if I need to take Plan B or not, and I have been on birth control for about six months now. Thanks.