The only CURE for a sinus infection is an antibiotic which requires a prescription from a licensed health professional.
Neti pots have really emerged on the scene since Dr. Oz showed them on Oprah, and the company who introduced it to the market has done a good job of conducting studies and released clinical information to validate their uses. The KEY thing you have to do to properly use a neti pot is to make sure you have sterile water - otherwise, you're introducing more bacterial into the cavity.
Pseudoephedrine simply helps reduce inflammation of nasal passages.
Mucinex is an expectorant.
I'd ask a pharmacist about all the suggestions you've received to see what they recommend as customers in pharmacies tend to be much more open with pharmacists than they are their own physicians.
Most pharmacies have several different antibiotics on their $4 generic list. The question is how many are FDA approved to treat sinus infections vs. other bacterial conditions.