I hate that min 3 bet...but you did give up the iniative easily to it .
Personally Im 4 betting...Im UTG Im supposed to be the one with the good hand. As im going to be oop its going to be a testing 4 bet as well. I'll cross the all in pre bridge if it happens.
As you played it the shove is very polarising to nuts or air. We are basically repping a set of jacks or tens maybe 888
. I think he probably folds one pair hands. You better hope that's what he had and that he's not stubborn ....Its difficult to comment without knowing the player type and how much of a calling station he is...
Wouldnt full pot also get the job done to save some if you are wrong.