Training while on antibiotics

I have bad allergies, which give me frequent sinus infections(4-5x per year, and I take Claritin). My ENT doctor always tries to get me to take antibiotics, and I sometimes give in after enough suffering. He recently suggested a 3 to 6 month profilactic dose of Biaxin to break the chronic cycle I’m in with sinusitis. I’m hesitant because I don’t know if:
1)antibiotics slow the body’s recovery rate after training. Should I even bother training while taking the stuff?
2)antibiotics will interfere with any of the supplements I’m taking, like Myotsat, Mag-10, or creatine. I don’t want to keep taking supplements if antibiotics are going to negate their effects.
3)among many other concerns, I’m worried about my body’s own resistance being lowered by taking too much of that crap.

If anyone at T-mag and/or in the Forum has any insight for me, it would be greatly appreciated…Thanks-