cbet larger on the flop. your cbet on the flop is just under half pot, and I usually take that as a pretty good sign of a draw (not always, but it seems to be a pretty good indicator so far) I pretty much always cbet 60% - 70% of the pot so i think a 5bb cbet would be more appropriate.
I think C9 is right about checking the turn, especially because it keeps a wider range in. unless you are betting as a bluff, in which case your line doesnt tell the right story. if you are in fact bluffing
here then a properly sized cbet on the flop would have been much more helpful in making it look like you flopped a flush. if you are value betting, then your trying to get value on a draw, and thats not the right spot to value bet. if youre not betting for a bluff, or for value then you have no valid reason to bet. and you have very valid reasons to check here (pot control, range manipulation... but dont worry about that, just know that if you dont have a valid reason to bet, then check)
as far as whether or not the call is right. you have 19% chance of making a winning hand, and you are only paying 18.5% of the pot to call. factor in implied odds and you definitely have the right odds to call but only barely. this is a pretty marginal spot.
you would be getting better odds if you checked because villain wouldnt have been able to correctly bet as much and it would be more positive EV to call then.
i dont think its right to count your outs for the gutshot because villain is representing a made flush. and we cant assume its a bluff because raising on the turn is a very strong move and we dont have any info on villain. ... or maybe a made 10 high straight, in which case we split if we make the 3 outs... so really we should only be looking at our outs for the flush because we would have the highest flush if we make it
dont be afraid hit the time bank and open up your calculator or use the calculator on your phone to calculate your pot odds in spots like this. (if you have time. usually you have time if youre on 1 or 2 tables. if you have 4 tables, then maybe not.)