Well the analysis of 12 Kxh2 Ng4+ 13 Kg3! (Kg1? Qh4 probably wins, keep in mind I'm not playing this out on a board.) is critical. Then 13...Qg5 is probably the only way to continue, then 14 Ne4! from the looks of it seem good for white, and my gut is that white can hold the position, but I can't be sure.
Edit: never mind, after 14...Qg6 I think the knight is attacked and the discovery is threatened. White needs to play 14 f4 and create a flight square for his king. I don't have a board, so somebody else can figure out what happens after f4 lol. This type of sacrifice is very common, and the moves are typical for this sac. It seems that most of your pieces aren't prepared enough to mate the king.
I enjoyed this game at best, not because I won it, but because I was doing something uncertain and new for me (I am quite new at chess). Turning point is move 11: I am playing black and I think my position is not great, so I try to "brake" the game somehow...
I have to confess that I started my plan but I did not see its end clearly, so things may have gone wrong (?). Then question is: "can white escape my attack and, eventually, win the game?"
Any comments are welcome!