To be honest, i think you got a bit lucky to end up with those 2 center pawns. But good playing.
Couple of thoughts:
4. Nc3, I don't like it, that knight gets in the way, and prevents setting up the stonewall defense with c3. My knight usually comes out via Nbd2, where it also can be used to defend the important e4 square.
Another suggestion might be: 4. b4 --The bird/orangtuan attack, setting up the queen fianchetto bishop.
Larsen v. Daly 1962 4. b4 Bg7 5. Bb2 O-O 6. Be2 Bg4 7. O-O Nbd7 8. c4 .....
Edit: some other games from my DB that varied from your 4. Nc3 that you might want to peruse for future games.
Tengu who was a pretty decent bird player around these parts tried his Nc3 in this game and blundered it a way. A common prolem I would gather against the fianchetto'd bishop.
MPP went with b3 and the fianchetto in this game: Game 2674249
Trad who was a decent enough bird player, went with castling earlier Game 1238104
5. d4. If you are gonna go with the stonewall, you should have had c3 in position making ..c5 less of a threat.
14. h3 I disagree that it is not a "great move". I think it is thematic as the kingside pawn attack is pretty much a given in the bird.