I agree with the above reply. It's amazing when you get "stuck" overanalyzing something how drastically it can affect us. If you start focusing on your breathing, the same thing happens. Before long, you feel like you have to control your breathing, or like your breathing isn't right.
Thankfully, most of these functions are automatic and don't need any help from us. Even if it "feels" funny, you can be assured that there's nothing wrong.
If you haven't recently, go see your doc, have a thorough exam, and maybe ask for a referral to an ENT who can more closely assess your swallowing, just to reassure you that nothing is wrong. Then definitely start addressing the anxiety with a professional. Have you ever tried any therapy for your anxiety? Meds?
Keep us updated!
This could definitely be a sign of anxiety. I used to have a pretty bad aversion to swallowing pills, and sometimes I would put the pill in my mouth and "forget" how to swallow. I just couldn't bring myself to do it. I'd take the pill out and then suddenly I could swallow again. When this happens, is your appetite suppressed at all? Do you feel a wave of nausea when you swallow? Those might be signs of anxiety. If you are concerned go see a doctor. They can check to make sure there's nothing physically wrong with your throat when you swallow.