Antibiotics for bacterial infection, on birth control 1 yr, not missed pills, had unprotected sex day started antibiotics. nausea and cramps day afte?

Probably infection: I doubt that the nausea and cramping are due to the birth control pills. The infection may be causing them ( you did not say what kind of infection) or , more likely the antibiotics. Antibiotics frequently cause stomach upset and cramping. Some do interfere with contraception though so to be safe use condoms or another backup for the rest of this package.