You sound like you have good communication with your doctor. Why not ask her or him these questions. If the doctor isn't worried, then I wouldn't be worried either.
Birth control pills are a pretty reliable form of birth control if you are taking them carefully and not making any mistakes (there a less then 1% per year chance that you can get pregnant even taking the pill; it is small but not impossible).
If you are worried about changing pill, using a condom during this time won't hurt anything and will reduce the chance of pregnancy even further.
I assume you already know that the pill does nothing prevent STD's if your partner is with anyone else.