Another Loss

I continue to reflect on my experiences from 2007. This example comes from one of the more frustrating games I had that year. I was white, and had had a very memorable game against a prominent master up until the endgame, which I was continuing to win, but we were in a time scramble.Here, black to move played 36...Rf8 and I completely neglected to look for problems. I was down to a few minutes, and was very very nervous - as one is wont to be when beating a hotshot master.
37.a7 Rf4
and now my heart stopped. It looked to me like I was losing all of a sudden and there was nothing I could do about it. All I could find was
38.Qf3?? Rh4+
39.Qh3 Rxh3+
40.gxh3 Qxh3+
41.Kg1 Qg3+
43.Kh2 Qa8
and I'm toast because the black king can catch the c-pawn.
If I had been a little tactically sharper though... and maybe if there had been a little more time, I would have found the saving move,
38.Qc7!
after which follows
38... Rh4+
39.Qh2 Rxh2
40.Kxh2 Qf4+
41.Kg1
and black runs out of checks and cannot stop the a-pawn.
I guess it remains anyone's guess whether I could have then won the won game with the little bit of time I had, but the point is that I blundered and missed a critical ONLY move in a time scramble. Looks to me like more weak tactics.