Yea, provided he didn't put you on a set (maybe TpTk), he had 9 outs for a flush, and another . . . what, five for two pair/trips?
Giving him 14 outs (x4) for a 56% chance to beat AJs. Since we know you had a set, and short of running 3's or K's or a combo of the two, let's just count his flush outs.
9 outs, (x4) for a 36% chance to make a flush.
Now let's look at the pot size after you shove.
20.2 moneys in the pot already,
7.5 moneys to call, or almost a 3:1.
If he doesn't put you on a set, then he's absolutely making the right play. If he puts you on a set, then his call is correct on the river anyway, barring your fullhouse redraw that I don't know how to calculate.
Stu is right, you didn't bet enough on that board.
That board is soaking wet and you played your monster too slow, but I doubt villain is going to pay you off in any way shape or form on this hand.
Since you can't see his hand, you don't know to jam, which I would consider the right move, and even then you're getting your money in bad to 33 or JJ. So you bet half the pot.
What draws are you shaking with a half-pot bet in a multiway pot?
None.
Spade draws and heart draws.
He raises, because if you have the nut FD he is ahead with his pair, you jam, and he has no choice.