Did I play it right?

Hi.

Just wondering if I played this right?

online tourny paying 3 places.
I made it to position 3 and was first to act on the next hand after 4th place going out.

Had KJ off, so pushed my shorter stack all in hoping for fold fold.

SB folded BB called with a few thousand more chips than me.

Guess what...BB had AA and they held up.

Got $200 for my troubles, which im pretty pleased with, but was kicking myself. Should I have waited to see if better cards came in my BB or did shoving at that stage with those cards make sense?

The blinds were huge at that stage.

Even if you had QQ or KK you still would have been dog. Youre SS you got to move. You just got unlucky. I would have done the same. If Im Big Stack I would wait.