I have same problem, my cough started a YEAR gone JUNE, after I had an infection in my throat and ear, and pains in my head. Got antib's to clear this up which it did but left with this stupid gagging cough now, that happens anytime and anywhere. Been for chest xray, camera up nose to throat, treated for silents reflux with Gastro tablets. Nothing came to light - been basically told me now by GP "can't do anymore for me so will have to put up with it!!"
If you can get some leeway with your cough i'd be willing to travel anywhere to see someone else to help me get some relief!
Just out of curiosity what meds are you taking??
Cheers - Sheila