Sounds like it could be due to post nasal drip.
Try using a sinus rinse such as the neti pot or sinucleanse.
Another possibility is from an allergy...such as milk, which will cause mucus build up.
With either of these you aren't normally prescribed anything except for allergy sprays, allergy pills, or told to use a sinus rinse and avoid whatever it is that is causing it...so I've learned over the years lol.
I suggest you stop dairy for a week and observe the results. The problem may clear completely and you will have your answer. For me, milk, yogurt and ice cream have the biggest impact. There are non-dairy substitutes available.