This was my first hand at the table - never seen MP2 before. His min raise is what made me think he didn't have AA or KK, and I didn't have to worry about anything else on the flop. Did I play the flop badly though?

PokerRoom No-Limit Hold'em, $0.50 BB (9 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

MP3 ($40.90)
CO ($3.25)
Button ($27.45)
SB ($22.20)
Hero ($25.00)
UTG ($22.10)
UTG+1 ($62.10)
MP1 ($3.95)
MP2 ($44.95)

Preflop: Hero is BB with Q, Q.
3 folds, MP2 raises to $1, 1 fold, CO raises to $1.75, 2 folds, Hero raises to $4.25, MP2 raises to $6.75, CO calls $1.50 (All-In), Hero calls $2.50.

Flop: ($16.90) 2, 2, 5 (3 players, 1 all-in)
Hero bets $5, MP2 raises to $20, Hero calls $13.25 (All-In).

Turn: ($55.15) 9 (3 players, 2 all-in)

River: ($55.15) 6 (3 players, 2 all-in)

Final Pot: $55.15