NL 500 (live) AhKh flop flush draw OOP against TAG preflop raiser

[schwerd2]

I am in the BB with AhKh. 2 people limp and TAG raises to $30 from MP. Folds to me and I call in the BB. I know I could have re-raised here, but lets discuss the hand from this point on.

I have $800, TAG has me covered.

Flop comes 2 962 two hearts, I check to TAG and he bets the pot. I didn't know what to do at this point? Just call or check-raise?

I check-raised to $180 and he thinks and just calls. At this point I'm pretty sure he has at least QQ.

I miss the turn and check, he checks behind. I thought about shoving but I don't know if he would be able to lay down a big overpair to the board at this point.

I miss the river and we check it down.