I have had this happen many times, can't swallow, can't speak without excruciating pain. Usually occurs when I am laying on my side and yawn. I have searched for help on the internet while massaging my throat and usually within a minute or 2 it would pop back in place. That has not worked very well but I finally found the answer that has worked every single time for me.
OPEN YOUR MOUTH AND SAY "Ahh" like the doctor tells you to.
Works instantly every time.
I actually found that answer in another forum. A girl had to go to the hospital because she was in so much pain, and when the doctor finally got to her, he told her to open her mouth and say ahh. It went away instantly. Excellent doctor :P