I don't see any reason to 3bet AQ pre, and shoving the turn seems retarded. Try to have reasons for doing things rather than mashing buttons. This is a great spot to call a lot in the whole hand.

3betting is not turning your hand into a bluff, if he 4 bets your beat and can fold, he's not 4 betting with worse
The fact that he only 4 bets better is an argument for having a bluff hand when we 3bet here, not a reason to 3bet a good hand.