1/3 NLHE - Thoughts on Backraising

I get dealt QQ on the button on my 5th hand at the table. UTG limps $3 and so do 3 other players before it gets to me, so I raise it to $20. It folds back to the original UTG limper, who 3 bets to $70. It folds around to me. At this point, I still have my $200 buy-in and don’t have any info on this player. Am I safe to assume a back raise in this spot is only AA, KK, AK? Is there any way I get away from this?

I tank and eventually shove all in. He snap calls with AA, and the board comes out clean and he scoops the pot. Just a cooler?