I think you're right in that your 37th move was the one that lost the win. A good thing to do in those situations, when you have an extra pawn on one side of the board, is to try to keep all of your pawns in line as much as possible.
Still, congratulations for getting a draw against such a higher-rated player. At least you didn't lose...
Ok, i'm proud of myself =) i drew a game with someone rated almost 600 points higher than me! Why is this in endgame study, then, instead of games showcase? Because i'm CERTAIN that I missed a win somewhere. Please tell if you find one, or just comment on other moves you'd've changed. Thanx!=)