I was in a losing position after a blunder. However, I pulled off a draw. I know I could have won, but other than that, what do you guys think?
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It was a nice recovery after your blunder, but you had plenty of time at your 19th move and you only spent 3 seconds on 19. Nh4? and 15 seconds on 20. Qh5?? missing the mate starting with 20. Bxg7+. My guess is that you don't know enough mating patterns (the rook lift to e3->g3/h3 is pretty standard) and you would have won the game. Maybe take a bit more time?
The "blunder" was there for two moves and both sides missed it. 15...Bf6 would have won as well. So the real blunder was 14 d4 or even 13 exd5 instead of the better 13 cxd5 towards the centre.
After 19...gxh6 20 Qxh6+ Kg8 21 Re3 you win.
I think his mistake was 19...Kh8: with 19...Re8 instead he would have got a counterattack against your back row.