As you stated you should fold pre-flop.
If you don't hit as good as you did it's hard to defend almost any boards with 6,3. Even when you hit you can be beaten (even if it is less chance for that HU with short stacks).
I think he picked the wrong starting hand to
bluff with. If he had the ace of hearts it would take the nut flush away from you and would have been a semi-bluff on turn instead of a pure bluff. An ace is often good to check down HU so he could have bluffed with worse
hands or a draw instead.
So both check or bet the the flop is fine from villain. You almost don't have the
odds to call with your low flush draw. But once you do call the only hands he can bluff you off is probably better aces and pairs lower than a queen. Maybe a bad queen also? I would have checked the turn myself most off the time.