I feel as if I don't use my Queen enough.


Forget about bringing out your queen earlier. I think you need to study basic endgames. Here, you threw away a draw.
If you knew anything about basic king and pawn endgames, it would have been obvious to you that trading rooks here would be a quick way to lose.
There two ways to draw here. Trading the rooks loses by force. It brings about a basic king and pawn endgame where you are just lost.
If you go back through this game, you made numerous mistakes in this basic endgame.