Tricky Position in the Late Mid-Game

I got into this position earlier this evening playing online.  I had played pretty well to this point, but was now in a bind.  I was completely unsure of what to do; you'll notice my queen is tied to the g-pawn, as leaving it unprotected would lead to ...Qxg2#.  I got into this position and had no ideas; I panicked and blundered with Rxf4, losing the game.

Looking at it now, I'm still somewhat stumped, the only thing coming to mind is g3 to try to prompt a rook & queen exchange to open the game up and get my king out of a tight spot.  Any thoughts?

Well, I'm not a great player, But Houdini found (in less than a second) Bxb6! with a totally winning game for White.

 That was a thought of mine, but I didn't think it would pan out in time.

1. Bxb6, ...

If 1. ..., axb6?? 2. Qxb6+, Kc8 3. Qc6+, K(any) 4. Ra8# (nice puzzle)

If 1. ..., Bh4 2. Bxa7+, Kc8 3. Qa2, ..

When I first looked at that position, my gut said Bxb6. But then I did some calculations, and for some reason I thought the queen would not capture with check, and thus would be leaving the defense of the g2 square. This must prove I'm up way past my bed time, or my rating is just not accurate.

Thanks for the input, everyone.  I was disappointed because I had played so well up until this point and I thought I ended up in a bad position.  I guess I was close to mating after all.