You mentioned that you don't have anxiety anymore, but you do. The tightness in the throat is a symptom of anxiety. Allow the tightness/gagging to happen. Don't add anymore fear to it. Just accept it as best as you can. Eventually, you will not have this symptom any longer.
You need to do some relaxation techniques when you DON'T have the tightness and gagging. It will help keep the feelings controllable. Good luck!
Generalized Anxiety Disorder
60 mg. Prozac, Ativan as needed.
"Nothing makes us so lonely as our secrets." Paul Tournier