Ask a pharmacist if [exact name of antibiotic] interacts negatively with and diminishes the effectiveness of [exact name of birth-control pill]. Or go on the website of the birth-control pill and see if they have a drug-interactions section, and look for your antibiotic.
If you are not telling your boyfriend that you are on an antibiotic because you got an STD from someone else, I don't think that is a good idea. Your boyfriend should be warned if he is being exposed to something from you, (and if you aren't done with your antibiotics yet, he could be). And if he gets it from you and is not treated, he can give it right back to you after your antibiotic run is over.
wait to see if you miss your next cycle, if you do then take a pregnancy test. because antibiotics do mess with birth control pills.