I assume folding here after the shove is the correct option.
There is a chance he is bluffing
, but there is a high chance he turns over some sort of ace. Also a possibility he has tens or jacks and reacted accordingly to your check.
To critique you i'd say why in the world would all of the money not be in pre-flop? I feel like that was a terrible move.
The check on the flop I guess I understand because of the ace, but that's exactly why that's even more so of a reason to move in pre-flop!
First you're out of position for one thing, second he probably does not have aces or kings, and if he does unlucky you, and he's committed to the pot so you want him in there! Third, if it does end up being a safe flop for you, chances are it's no good for him, and he miight be able to get away from it, losing you money.
Due to your mistakes pre-flop, you are forced to check fold here imo.