High pair against flush draw, or is it a set?

I think I loose too much to this kind of situation (nearly 200$ yesterday).
Any advice?

NL 1/0.5$ cahs game.
I hold AA, KK or QQ and raise several limpers and end up against one or two callers.

Flop comes T:spade:8:spade:5:diamond: and I bet the pot and get called. Turn is J:heart:. I bet 2/3 pot and get miniraised (20-40 or 30-60 etc.). What do I do?

It seems like every time I push they hold a set here. If I just call I will often be pot committed anyway. Do you guys fold in these situations?

I'm be more likely to fold to a turn raise than to a flop raise, if you bet strong on turn and get raised it usually means they beat an overpair I think. Try to figure out how the various players at your tables play draws though. Some are passive with them, some are pretty aggro, most that are aggro are aggro on flop though and not on turn.