Upon trading Rooks on move 33, you have a clear advantage, being up a pawn, and otherwise equal with both sides having doubled pawns vs three opposing pawns, except your doubled pawns have another pawn to support them.
43...Kb5
The problem here is that after 44.Kd4, suddenly you can't move your king without losing your c pawn, nor can you play b5 to defend it with your b pawn.
Thing is...it doesn't matter. if you then played Ka4, you could then capture the a pawn, and take white's c pawn if they go for your b pawn, and then your can force your way through the doubled pawns even without your king, because white's king is on the complete opposite corner of the board. Sometimes it's good to stop and think, "what if I just go for it?"
51...c3
In cases like this the rule of thumb is "what happens after these pieces trade?". In this case, you can see ahead of time that there's going to be trade of queens if you both wind up promoting due to the king's position. So think to yourself of where you want your king to be after that trade happens--in this case, closer to white's remaining pawn. the king has nothing to contribute going closer to a pawn that you can't keep from promoting anyway.
Fortunately your opponent didn't see the draw. Good job though.
I was lucky to win this endgame after my opponent missed an obvious move and thought he was going to lose his queen. My opponent is a low-rated adult who entered the game with a provisional USCF rating. I believe the game would have been a draw had he found the right move. I would like to know if I could have won this endgame, and how I should have converted my advantage before blowing it. This was an OTB game, 30+0 with no delay. At the end, I had 2 minutes 50 seconds left and my opponent had a little over 2 minutes left. I have not done the computer analysis.