I am on this website because I, too, am trying to figure out if I have problems with gluten. So, I cant tell you my experience with it or help you in that field.
I do remember something I read about smoking years ago. Are you still smoking? Do you ever smoke after drinking alcohol? I don't know if this is your problem, but when you drink alcohol, it changes the way the cells in your throat absorb things. So if you drink and then smoke within a certain period of time, the smoke penetrates your throat cells alot more then if you didn't drink. The irritation from smoking could be enough to make your throat swell and cause problems with swallowing. Even if you do not drink, I would think that smoking can still cause inflammation in the nose/throat area. If you have quit smoking then that is different. Has your doctor looked in your throat at all? Does it seem to be inflamed?

There was this show on tv that spoke about silent acid reflux causing swelling and permanent damage to the throat. I would maybe look into that to see if your symptoms look familiar. I am not a doctor so please don't take any of what I said as "medical advice." They are just suggestions.

I don't know much about gluten intolerance, but I think I read that some people get acid reflux from it. So, if you were indeed having problems with gluten, maybe you are having "silent" acid reflux and would benefit from trying to take an acid reducer before going to sleep every day for a period of time. I would ask your doctor about it.