Thanks for adding the details about the blinds, didn't realize you were already at 10xBB as a shorter stack. I'd vote that your call was a weak call, possibly considered bad but it's preference fo style. You're technically a short stack at this point with less than 10 big blinds to your name (factoring in the ante). So realistically you are at the point of needing to be the aggressor, not the caller. Q10 is a hand you can raise with but not in this position with the action in front of you of a shove (even with a shorter stack) and a caller who has you stacked. i think your two plays here are reshoving (bad idea with that holding) or folding, probably a better play to let someone else knock out the player and avoid you risking your stack or tripling up another player. Even after the flop you can't feel too strongly about a 10 kicker since you are dominated by AQ, KQ, QJ, all likely holdings for a player that would call UTG and willing to risk 10% of his stack to eliminate a player. Long story short, i don't think you should have even called the preflop bet. That could have saved your stack as well as avoided potential bad situations like this.

Fish