Welcome to the future, where most microbes are antibiotic-resistant. Or, you could just have an encapsulated mass of infected mucus, which antibiotics may not penetrate. At any rate, a Flip-Turn Sinus Flush will remove the mass of mucus from all of your sinuses, and stop the secondary infection from it going into your lungs.
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 with the shower running.
If you are over age 45, I recommend you try the kneeling down method.
btw, there is often a link between asthma and sinus problems. One the doctors I mention theorizes that the link is due to a fungus, but nothing has been established yet.
good luck