QQ vs. Big Blind

[wallofchips]

I'm playing .50/1.00 NL, I just sat down. I have QQ in the SB everyone folds I make it $3, the BB makes it $5. I consider flat calling because I don't want to invest a lot out of position. However, I decide that the BB would raise with a lot of hands thinking I'm on a steal, so I decide to make it $15. He flat calls and the flop is Axx, I check and fold. I'm wondering if I could have played this better or if I just have to lose when an Ace comes...