How Long Does A Sperm Take To Fertilize An Egg After Sex?

My question is about pregnancy. How long does it take after sex for a sperm to fertilize an egg? Also is it possible for 2 people to have sex, The egg is fertilized,the woman has her period, and still be pregnant?

Idk if this helps any but here's the scenario. My Girlfriend and i had sex about 4 or 5 days ago. 2 days after we had sex she had her period. now after it was over shes complaining of something that sounds a lot like morning sickness. Im wondering if its possible if she is pregnant or not. We did use a condom during sex and she is not on birth control. please help