Well, without a detailed clinical evaluation it would be difficult to determine the cause of your symptoms. Possible causes of the throat pain and the exaggerated gag reflex that may need to be considered include infections, inflammations, muscular issues, psychological issues, growths/ masses etc. Solitary exaggerated gag reflex is unlikely to be a result of neurological issues while that pain/ discomfort could be a related symptom. I suggest considering a detailed evaluation by an internist initially and depending on the cause diagnosed/ suspected it can be managed accordingly or specialist (rheumatology/ neurology) may be sought.
Hope this is helpful.