I think check call the flop is fine, maybe check raise if there's flush and straight draw possibilities. I can see the merit of a check raise as the board is semi-wet, but I don't **** my pants over that board personally.
Definitely check raising the turn though, would lead for value if villain shuts down on the turn though, don't want to risk a free river.
As played I call here, you just got unlucky if villain was barrelling ace high on the flop and turn
Disclaimer: still a fish