You shouldnât take codeine if you're allergic to it (or to any other ingredients in the drug) or have trouble breathing. If you experience any of the following after starting codeine, talk to your doctor, as you may be allergic to the drug: Itching; Rash; Hives. Before taking codeine, tell you doctor if you have: Kidney or liver problems; Seizures
Mucinex does help thin out mucus but doesn't do anything to reduce the swelling and inflammation in your sinuses. There are several medical options for reducing this inflammation: 1. Try switching from a neti pot to a NeilMed Sinus Rinse bottle.
Thus the mucus is forced down the back of the throat. When the mucus become trapped in the sinuses/nose it gets thicker, and it is this thicker tenacious mucus that is getting stuck on the back of your throat.   You can try mucinex or sinuswars2 to treat this problem.