I think people put others on a flush draw way too often. Having two suited cards and flopping/turning the flush draw is not as common as people think it is.
Shovinc turn is alright though. Not many other options we have, but I find that you played the hand quite interestingly.
On this type of board I'm probably c-betting though. We don't really rep anything other than KK, AK, and KQ, and I expect to get floated a lot on this type of board texture. Any PP and some A highs, and of course the flush draw. And I would check-raise turn, or maybe mess around and flat turn, then make a min-bet/small blocking bet OTR to induce some spazz.