QQ on AQJ board

[jonnyv]

Utg with QQ, I raise 4x BB, mp calls, and button calls. Flop is AQJ rainbow. I bet half the pot, mp folds, and the button puts in a 20x reraise. The button is a very srong player and has been running the table over. He always has the goods and he knows that I have only shown down premium High pairs and knows this board hit me. If I fold, I loose very little, calling here, he will put me all in on the turn as I will be pot commited and cannot fold. Raising all in is my best play as if I am behind I have two rounds to hit my fh barring he has AA. I misplay and just call. He puts me all in on the turn and I call. The board dosn't pair and he takes it down with the nut straight.
I don't know why this hand bothers me so much. I suspected I was behind but really don't think I could fold with a set and outs to a fh. Knowing you are beat here on the flop, who folds and who goes all in?