[2NL] AQo. TPTK facing shove on turn... (Short Stack)

Villain was 50/14 through 36 hands. Folded to 100% (3/3) cbets on flop. Other than that not much to go on.

PokerStars No-Limit Hold'em, $0.02 BB (6 handed) - PokerStars Converter Tool from FlopTurnRiver.com

SB ($1.08)
BB ($0.61)
UTG ($0.86)
Hero (MP) ($2.25)
CO ($0.70)
Button ($0.83)

Preflop: Hero is MP with A, Q
1 fold, Hero bets $0.06, CO calls $0.06, 3 folds

Flop: ($0.15) 7, 5, A (2 players)
Hero bets $0.09, CO calls $0.09

Turn: ($0.33) 2 (2 players)
Hero bets $0.19, CO raises to $0.55 (All-In), Hero ???

This was the first time I had seen him raise post-flop at all. It stinks of a flush but can I call with TP and the Qd?

ok, so you think he has a flush.
what percentage of his flushes include Kd.
How many outs do you have vs the non-nut flush?
how about vs A2? vs 34?
how often do you need to win at showdown after calling here?
answer these and you'll probably end up with an answer to your question.

Your question shouldn't be what to do now (although if you don't know you should figure that out, too).

This is pretty simple. Give villain a range, figure out how much equity you have versus said range. Figure out if it's enough to call.

What is the villains range you ask? Your guess is as good as mine. Try different ranges, see where the cutoff points are for a call. Nobody on this forum should be able to do a better job of this then you as long as you put in the time and effort to solve this problem.

edit: Okay maybe in game your range estimation is a bit off, maybe even out of game but if you don't guess at ranges on your own how will you ever improve. You aren't a complete beginner so I'm sure you have a decent grasp on how to estimate ranges yourself.