These are tough spots not to go broke when the flop is all rags.
You raised from UTG so your image on the table plays a huge role, because villain is in MP and decided to 3bet you for the minimum (which is very suspicious, but doesn't always mean AA or KK). So we need to also consider his image and what read you have on him.
If he's been loose well then...he most likely gets me here PF because I'm sure I would 4bet to about 28/30k. Whatever happens after that depends on the size of his stack but even if he flat calls the 4bet I'm going all-in on this flop and I get nailed. There just is no way out for me with QQ vs a loose player, min 3bet or not. It's probably a weakness of mine not being able to read danger against that type of player, which is why I pay off their monsters just about always
.
Even if I don't 4bet this PF (occasionally I might want to see a flop even vs loose player just to protect vs AK type of
hands, but don't consider this a standard play vs a LAG) I know I'll likely check/shove his c-bet, so again he gets my ass either way.
How many chips did your opponent have and what, if any, read did you have on him?
If he's been tight there is a chance I can escape this because of his min 3bet, but I'm not sure. Did you see him 3bet before this hand? Has he gone to showdown? Has he been very active?
In honesty its very hard not to go broke on that flop, but in some (not many) cases its possible.
Also, in the future, if you want to have objective opinions from the other members, next time leave out the end result.