I'm not willing to give specific advice about a game you are currently playing, and since you didn't say where his pieces were, I probably couldn't anyway.
But the general rule is that early in the game, you need to protect your king. In the mid-game, you still need to protect your king. But near the end of the game, when most of the major pieces are off the board, you usually have to use your king.
Often to help defend a pawn so it can promote.
Or so that you can take one of your oppoents pieces when he captures that pawn to stop it from promoting.
Of perhaps you need to use your king to stop your opponents pawns from promoting.
If you study basic endgames, you will find that the king is required to help with the checkmate itself. Rook and King vs King, for instance, is a basic mate that everyone should know how to do. Without the king helping, the rook will not be able to force mate.
In your case, since both queens are still on the board, you should probably not develop your king at this point.
This is my first game. My brother who has played in the past is winning, as far as pieces go. He has only lost a two pawns and a rook. I have lost 2 bishops, 2 pawns, and a knight. I am white. It is my move. I have a King on F1, a knight on B1, a pawn on D2 and F2. A pawn of B3 and a rook on F3. A pawn on A4 and C4 and a queen on H4. And I have a pawn on G6. Would it make sense for me to move my King to H1 in the corner? My thinking is he would then only be able to attack my King from the left.
Please tell me if my thinking is correct. I apologize in advance for my lack of knowledge, but I have bought 2 books on the game and I am learning.
Thank you for your advice.