How would you play it?

[Tyler13jack]

1/2 NL with a full table. The table is generally showing good cards but many players are chasing draws regardless of the odds. Player 1 (loose and fast) raises 2 spots off the bb to $15. He had been raising about 20% of pots preflop. The player to my right calls $15. I get QQ and raise to $50. A relatively inexperienced player on my left calls the $50. He picked up quads and backed into a full house a few hands earlier so he's got a good number of chips. The player on the button calls after some deliberation, the initial raiser folds and the player to my right calls after stating he is getting good enough odds. There is now $200 in the pot.

4 players to the flop. It comes 8 5 3 rainbow and player 1 checks. I have $185 after my preflop raise. My thinking is there are 3 plays. Check, All in, or some sort of small bet. If I check, I'm allowing any AK to take a free one or let another small pair hit a set. I didn't like that choice.

Option 2, Any small bet will give everyone odds to call and if an A or K comes on the turn I'm gonna be pot stuck and have to make a tough lay down or be priced into calling while an overcard is on the board. I didn't like that either

Option 3, (which is what I took) was all in for $185. The player to my left calls and shows AA. The player on the button folds JJ and the player to my right folds his unknown cards.

Now I could just chalk it up to running into aces but while I was aware someone could have picked up AA or KK especially with the smooth call to my left but being in the position I was in, I couldn't check and let someone peel off an Ace or a King. So was my play correct?