Why did you lead the flop so strong? You hit a set and the pflop raiser is behind? You think the 7xbb raise pflop could be with QJ or 87?
IMO your play is not optimal, but I wouldn't beat yourself up....your push is not necessarily bad.
Having hit such a strong hand you want all the money in the middle. So, instead of all-in, the optimal play should reraise large enough to allow villain to make a mistake either by (1) calling without odds
or (2) making a bigger mistake and trying to push you off your hand by reraising. By shoving all-in villain can still make mistake #1, but you have taken away mistake #2.
So if you raise to $2.60 even if on a draw villain is making a mistake to call. The fear is what if villain calls and a scare card hits the board? Well you have no idea villain is on a draw, your guessing. You are representing AA. Regardless of what hits the board, you are going to lead out and value bet the turn. If villain did happen to hit one of their outs they are not getting value on their postflop call because you made sure with the $2.60 reraise the call was not worth the draw.