flopped nut flush, then almost gave it away

Playing 5-10 at B&M last night; in MP, am dealt AdQd. I'm down to my last $70 and have been swinging and missing all night with AK and AQ. Plus, two loose players are behind me, one of which is very LAG, so I limp. Two players to my left (including the LAG) limp as well. Then the button raises to $10. All three of us call.

The flop is a beautiful 7d-3d-9d. I mentally flog myself for failing to raise preflop, then check, planning to check-call the flop and check-raise the turn. Everyone checks to the button, who bets. All three of us call.

Turn is a--uh-oh--3. I stick with the strategy and check again. Check, check to the button, who--whoops--checks himself.

River is a--#@*!%--9.

Now LAG bets out. Button folds. I call, sickened. Other player folds.

Turns out LAG had neither a 9 nor 3--he was betting his ace high, and I won the pot after sheepishly turning over my flush.

Aside from failing to raise preflop (for the reasons I already stated), should I have check-raised the flop, at the risk of losing the LAG and the other player? Should I have led the turn after the board paired the first time? I had put the button on an overpair, which was likely given the board at that point, and didn't expect him to check behind me.