Trouble with getting mate
I was playing the computer at chess.com and I was playing pretty evenly. I need some help trying to figure this out. I tried to recreate what it was like from memory. I hope I didn't forget anything. Note: This isn't a puzzle (only a display). However if you find a solution, can you make it into a puzzle? It would be fun. Less moves would be better if it's possible. [I am playing as White and it is White's move: Is checkmate close? I don't know. Please find it.]
It was like my second time playing My Little Chess Partner on hard difficulty and I was playing pretty even. Then I got to this point. I felt so close. It felt like I was doing a puzzle, but I gave up. It was too hard. I couldn't figure out how to win and I didn't finish the game. It would be so cool if someone figures it out.
Little notes to see if it helps anybody.
1) There's a rook in a1 and an open file at H. The rook could possibly back up the queen at H.
2) My bishop (h5) can move the diagonal in front of the pawn (g6) and the pawn can't take because of a discovered check from my queen.
3) My b2 bishop is on the same diagonal as the king, but there are two black pawns in the way and each is protected by a queen or bishop.