So the situation comes up often enough. You hit a 15-out draw on the flop and you put your opponent on an overpair. What's the best way to handle this?

You're a 52% favourite (54% if your opponent doesn't hold a card of the suit, 50% if he does).

The problem I have with pushing, however, is that I don't push my made hands (sets or 2pair), so doesn't a push completely give away the fact that i'm on a draw?

Anyways, as I said, i'm unsure of how to play these hands, so any suggestions are encouraged. Below is an example of how I recently played one:

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Hero: [8d 9d], Small Blind
Villian: Mid Position
Other Guy: Late Position

PREFLOP
Villian raises 4x
Other Guy calls
Hero calls

FLOP [Jc Td 5d] - Pot $12
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Hero bets $6
Villain raises to $15
Other guy folds
Hero raises to $45
Villian raises another $21 (all-in)
Hero calls
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PS - yes, I realize that it's preferable to play such hands in position. Please spare me the standard (and annoying) "fold preflop" replies. Focus on the postflop action please.