50NL: 3bet flop with QQ

Poker Room skin
No Limit Holdem Ring game
Blinds: $0.25/$0.50
10 players
Converter

Pre-flop: (10 players) Hero is MP3 with Q :spade: Q :club:
5 folds, Hero raises to $2, CO folds, Button calls, SB raises to $7, BB folds, Hero calls, Button calls.

Flop: 7 :heart: 2 :club: T :club: ($21.5, 3 players)
SB bets $15, Hero calls, Button calls all-in $11.65.

Turn: A :spade: ($63.15, 2 players + 1 all-in - Main pot: $56.45, Sidepot 1: $6.7)
SB checks, Hero ???

SB was 15/11/5 (seemed to 3bet TT+)
I was not worried of short stack of course.
Is this a fold/push on the flop? Would you push the turn?

Put him on a range of hands, then fold the flop.
On the turn I think you're up against KK a lot with stuff like AK/AA getting cute thrown in sometimes. With the button already all-in, I'm less inclined to see value in betting though.

Flop can't be a fold.