What would happen to my body if I took 1/4 of a birth control pill every day?

It's not bad for your body, it's actually a known fact that antibiotics interfere with the pill. All doctors recommend is that you have protected sex if you are taking antibiotics while on the pill, as it may not be working properly as a contraception. Don't stop and start the pill, just take it as normal and things will be better once you have stopped taking antibiotics.