Main Event - Level 11 200/800/1600

I'm on the button with 7s7d and have 42K (26bb). I am short stack on table and can double through everyone. UTG +1 raises to 3500 plus 2 more callers, I call & bb calls = 20K in pot. Flop 10d 9d 7h... bb checks, orig raiser bets 11k, fold, fold and I shove 38K, bb shoves and orig raiser folds. bb shows 8s6d and I miss and fly home. Should I have pushed or bet pot on the button pre-flop and hope UTG +1 didn't have a big hand and call. Thought it was cheap to flop a set in position and could easily fold or bet if everyone checked to me. Any comments would be appreciated albeit it's hind-sight now.