I'm afraid there are no exercises that will improve palatal strength. A therapist might be useful in teaching adaptive techniques to prevent choking, make swallowing more efficient, which is something to consider.

I had such weakness that my palate would not elevate to protect my airway at all when I was at my weakest. I get treatment at a teaching hospital and several residents came in to gaze at my useless palate when I was in the hospital. They were amazed! Sigh...

If you haven't already done it, I would suggest you consider informing your neuro of this exacerbation. There might be something that can help.

Sorry you feel rotten.