Pills & Amoxicillin??

Okay so i am given amoxicillin for my throat infection and asked my doctor and pharmacist will the pill interfer with my birth control pill they both said yes and use back up protection, great cool, but ive also read that some people have gotten pregnant when they took their antibiotics but I really want to know is it possible for the antibiotics to cancel out my pill and cause me to get pregnant if I recently had sex without a condom on Wednesday?