If you"re turning your hand into a bluff, your c-bet was way too big..... you"ve left no room to fold, and the call is pretty much mandatory. You have 4300 left behind, and there is 9950 in the middle.
No problem with your preflop play or your bet/raise sizing..... If he 5bets (which he probably will with hands that beat you), you can easily fold. If he folds, you gain table image. If he calls, he is generally doing so with a worse hand than you, and even though your are out of position, you have the impetus in the hand.
When it comes to the flop, there is 3750 in the middle. Once you"ve c-bet, it"s unlikely that he shoves anything that you can beat.... by c-betting say 1500, you find out the same info as you do when you bet 3100 - the difference being that you can still fold.
Put yourself in his shoes, and imagine how strong your play would look if you 4b pre OOP, then make a c-bet of only a third of the pot on an Ace high flushed board - it makes it a tough move for him to bluff.
Given that you have committed yourself with the c-bet size, he should know that you are committed to call if he shoves, hence he"s only ever doing it with a hand that has you beat..... so, it"s pretty certain now that you are beat, but you are totally pot committed. I think you have to call and pray that hearts are live for you.