Birth control & Antibiotics

I've had a bad ear infection for several months now & have taken a Z pack (the go to antibiotic for me bc I'm allergic to penicillin) twice in the past few months with no luck. I've always been told certain antibiotics can cause your BC to be ineffective. (I know people who have gotten pregnant while on BC, while taking an antibiotic. I also know z pack isn't a very strong antibiotic so I was never really very worried when taking it, we were still a little more careful. But today I was prescribed Levaquin to try & finally knock this infection out! My doctor told me it was a very strong antibiotic. I've never taken it. I'm concerned with it being a stronger antibiotic that it may affect my BC: I take Ortho Tri-Cyclen. Does anyone know how this affects BC & my big question is how long it stays in your system even after taking it? I didn't think to ask my doc, so any info would be great! Thanks!