Mucinex is an expectorant, so it thins and loosens mucus. You can try it with Sudafed (the real stuff, not the phenylephrine crap that doesn't actually work), since that promotes drainage. And drink lots of water. (My doc said 2L/day minimum.) Of course, if you have a bacterial infection, that needs treatment. (But according to MedLinePlus, most sinus infections are viral anyway.)

Have you tried a neti pot? It sounds weird, pouring salt water up your nose, but it does a pretty good job of getting snot out. (I got a whole lot this morning, which I'm attributing to the Mucinex. I know, gross.)

I'm sorry your doctor is such an asshat! I hope you can find a good one soon.