Once you're called preflop, you don't enough fold equity on the flop and you pot committed yourself to the hand so you have to shove. Wasn't a big fan of any part of how the hand was played. Pre or Post flop.
Due to your stack size, I would have never 3 bet this hand, other than a shove preflop. Based soley on your stack size, I think there were 2 correct ways to play this hand pre-flop.
1. Flat the $8, take a flop. If you hit a A or K, then continue. If you miss, just dump the hand and look for a better spot.
2. Because you're pretty shallow stacked, just jam the AK preflop. You have enough fold equity here, but not on the flop.