My first game against an IM

Terrible blunder made by me in move 29. (Maybe an excuse is the time trouble, I was low on time and so was he.)

Other than the blunder, how can I improve in the way I played?

12. I played h3, giving up my bishop on b3, as I was not very happy with 12. Bc2 Nc4. On hindsight, the computer gives 12. e5! which I didn't see in the game.

What should have been the main plan for me throughout the game? I did not feel as if I had any potential of a kingside attack.

Don't listen to the computer. 12. e5? is ridiculously hard to play, and does not get a ! since there are about 5 moves equal to it. Now that 15. e5! maybe gets a !. It's not so hard to play and there aren't so many equal moves. You get to mess up his pawns, and recover your pawn on b7.

it was a blitz game?

@DrHack Thanks. Curiously, when I check the computer a second time, it no longer recommends 12. e5 as the top move. Yes, 15. e5 looks great!

@Oscar_Varela It was a rapid 10-0 game.

You were doing well.
Only 28 e5 and 29 Rxe5 (4.3 seconds) made you lose.
You still had more time than your opponent: 1 min 47 s.
You spend enough time on 28 e5, but it was wrong.
You played 29 Rxe5 too quickly, probably because you had erroneously planned it when you played 28 e5.

@tpr
Spot on comment. I was already planning 29. Rxe5?? when I played 28. e5.

That is typical. Never trust your own previous calculation. When you have time on your clock, check again.