Back in the 70s, I rode a police motorcycle for my department for 7 years. My sinuses were really in bad shape from infection. I finally agreed to surgery on my sinuses. My doctor opened the windows of my sinus cavities on both sides of my nose. The object was to let my sinuses drain out the front of my nose. But, as luck would have it, the drainage did the reverse and drained down the back of my throat, causing me to cough, especially at night and bedtime, when I laid down. Twice a year this happens and I rely on two medications for relief. Benedryl and codeine cough syrup. My faily doctor is familiar with my problem.
The point here is this: if Benedryl is helping to stop your cough, you may have the same problem I have with my sinuses. Are you a smoker?
Ten weeks is way too long to be coughing and not have medical attention.