What did I do wrong?
Believe me I have no business analyzing games, but on your move #13, I bet if you look at the chess analyzer, they would have said move your Rook on f1 to e1 instead of your queenside rook. And I'm not sure why, but when one does not take the opportunity to make that move, the computer analyzer almost always seems to consider it at least an inaccuracy if not a mistake...
10 Bxf4 was a mistake, as he could have replied ...c6, winning a piece.
You should have looked at 15 e6. He showed massive disrespect in leaving his king in the centre that long - when that happens, you should look for ways to rip open lines and checkmate him for such insolence!
Moves 21 and 24 were tactical errors losing material... and I just plain don't understand 27 Nxc4.
But 15 e6 was a winner man. You did reasonably well in the opening apart from that blunder on move 10, and 15 e6 was the way to cash in. That's the main lesson I would take out of the game if I were you, aside from the tactical errors you need to cut out.
On move 17 the position is screeming for you to play e6!. You have a lead in development and his king is still in the center. (Pay attention in class) :-) You want to blast things open and crush him like a bug. After 17. e6 it's impossible for me to find a reasonable defense. The e file is opening and white can double rooks, move his knights up.....or just look at his opoonent with a funny face. You're winning here.
I felt that I played incredibly well in the opening, considering my opponent's higher rating. However, I fell apart near the end. I suspect the culprit to be 21. Ne6, but I'm not sure.