Whose play was worse... Need help :(

[Raemius]

I'm in a two table freezeout. Starting chips are $5000, I'm sitting on about $6000. BB is sitting on about $3000. I'm dealt 2-2 in late position. I limp in, with about 2 otehr limpers. We see the flop

The flop comes 6[img]/images/graemlins/club.gif[/img] 2[img]/images/graemlins/club.gif[/img] 9[img]/images/graemlins/heart.gif[/img]

BB Bets $200, all others fold to me, I raise to $1200, putting him on a flush or straight draw, he pushes all in, I call. He flips Q[img]/images/graemlins/club.gif[/img] 3[img]/images/graemlins/club.gif[/img] He spikes a [img]/images/graemlins/club.gif[/img] on the turn and hits his flush. Teh board doesn't pair and I'm crippled.

Was my bet bad, was his push bad, or was my call of his all in bad. Where did I go wrong on this hand? Should I not have called the all-in? Should I not have limped with my ducks in late position?