Birth Control & Antibiotics help

So, I know antibiotics can increase the effectiveness of the pill and to use back up and all that. This might be a stupid question but I figured asking might put my mind ar ease. Ive been on the pill for 5 years now and I've always taken it correctly. My fiancee always pulls put as well. I had intercourse about 4 days ago (havent since then). A couple days later started having symptoms of a UTI. Im supposed to start antibiotics today. Ive heard things about sperm living in a womand body for days after sex. So I'm wondering if starting the antibiotics could still lead to pregnancy even starting them a few days after having intercourse.