Great pawn play at the end. Just goes to show that positional factors can trump material, even with little material on the board.
Endgame escape
Thank you for the comments!
You're absolutely right, I did feel much more comfortable after he traded.
I didn't always feel winning in the game, but you may be right. You can probably understand how uncomfortable I was a pawn down in an endgame! What do you think of the line 41...axb5 42.axb5 Rd5 43.Bd6 with the idea of c6? 43...Rxg5 44.c6 seems to leave Black in trouble, so I think he has to choose a less materialistic move, but I can't find a way for him to defend - for example, 43...b6 44.c6 Rxd6 45.c7 and the pawn can't be stopped. Am I missing a defense? I can't be sure in a position like this.

Class players are often bad at endings. You can win (or draw) a lot of bad positions in the endgame. I think endgame practice/study goes a long way in practical results.
I recently played in my state scholastic championships, and decided I'd post two or three of the games here. This is my second round game. I ended up a pawn down in the endgame, but managed to win it, preserving my chances to do well in the tournament.