Not joking – take a good whiff of fresh ground white horseradish. Every erve Pesach my mom and then my brother in later yeasrs, would grind it for the maror, and one whiff cured me of any sinus issues I might have had.
If you have something for such a duration of time, a doc visit IS in order. You might even need antibiotics if you have a sinus infection. The Neti pot is only good if you can coordinate yourself enough to actually use it correctly. I never could.
I never heard of any stricture on zinc before. ColdEeze helps me. Refuah shelaima. Vitamin C is useless IMO. But general good diet and sleeping patterns are crucial.