Sometimes a tooth problem will cause a sinus infection in the maxillary sinuses, which your doctor seems to have diagnosed. Antibiotics don't always work. I'd recommend going to a Walgreens or CVS and getting a Neilmed Sinus Rinse, as they work in the maxillaries, but if that doesn't work, a Sinus Flush usually does
http://www.medhelp.org/user_journals/show/2322
The Flip-Turn Sinus Flush is mildly risky, because you have to bend over to do it, preferably in a shower, but you can also do it outside on soft ground, or you can kneel down and lean over a bathtub, or perhaps a plastic basin or tub, with the shower running for steam.