Analysis please
Your opponent should have tried to keep the center and kingside locked. Black should instead expand on the queenside.
It looks tome like 13. ... f6 and 15. ... Rf8 are mistakes. Maybe after 13. ... f6 black could have tried to lock things down by putting his knight on f5 and pawns on g6 and h5.
Yes, you could have mated more quickly. 19. Rxh5+ Bh6 20. Rxh6+ Kg7 21. Qxg6#.
It's probably a worthwhile exercise to analyze the consequences of the piece sac 13. h5 hxg5 14. hxg6 where white now has the open h-file and Qh3 might lead to checkmate.
Actually, I think white won't mate after 14. ... Nxg6, but this could make for a good exercise in analysis.
I didn't evaluate this following move deeply but 18.Rxh5+ gxh5 19.Rh1 Qe8 20.Be2 somehow catches my attention right away, sorry can't help it to sometimes try to play a Nezshmedinov type combination
maybe no so good anyways, since it would be two rooks for the queen if the thing doesn't work out all the way, but the weak light squares around the black king kind of give me good hopes
note: there is nothing wrong with the way you played, and it was better than my fancy dubious combination anyways, you just didn't finish sooner haven missed Rxh5+ after Nxg6
one advice though try not to work much in these kind of games where you won rather easy, they don't realy teach you much