10. ... h6 looks like a mistake. Especially since white can probably just ignore the threat against the bishop and play 11. 0-0-0. If 11. ... hxg6 12. hxg6 the open h-file is likely deadly in this position.
As the game went, white showed it's also possible to simply retreat the bishop and take advantage of the h6 push by playing a pawn to g5 where it forces open a file. Once a kingside file is open in this position, white's attack is very hard to stop.
11. ... Qc7. Is it possible here to play 11. ... b4 followed by Nxe4?
13 Nbd7 was a definite error as it allowed him to play g5 attacking both your knight and your pawn, forcing you to exchange. Better may have been Ne8 or maybe Nh7. You also maybe should have considered trying to break the center open earlier as his king is just sitting there where as yours is castled away safely. Some kind of counterplay would have helped you.
That being said I dont play the sacilian so I don't know if you did something wrong in the opening.
I agree with the comments made previously. I think h6 did weaken your king-side, especially since white indicated a king-side interest by 9. h4. White could even imagine sacrificing the bishop in some lines (Bxh6) because of the queen on d2. Like you say, you could probably use that move to develop your queen-side or solidify your king side. I might have continued: Nbd7, or Bd7 followed by Nc6