I thought I was doing well, help me understand where I went wrong.

You started better than the other guy. You threw away your advantage attacking impatiently, specifically by hanging your knight and then the rook. Try to be more careful with making sure your pieces are protected before committing to a move.

Your concept knowledge is better than your opponent's. You develop pieces on the beginning while he pushes pawns, so you clearly got a superior position on the start

But you need to work on not hanging pieces.

You hang a knight on move 18

You hang a rook on move 23

You hang a rook on move 39 Maybe you got too confident?

You could have avoided those if you doublechecked if the squares you are going to are threatened or not before moving to them and if you asked yourself if the opponent was threatening something with his last move. You should try to keep those things in mind when making your moves during your games. It's ok to become confident when attaining a winning position, but never become incautious

10 minute rapid. I ran out of time, he still had 5+ mins left. 

U got a big advantage against ur opponent, but u got too confident:

u hung a knight and a rook

u gave ur valuable pawns for nothing.

If u got to a winning position, don't be incautious, like dis comment above me said.

Running out of time in Rapid is very rare. Except if u are lagging.

and also, look out for bishops and queens. Their long range attacks are pretty scary.

33.b4 is bad. Could've took his g-pawn.

Wanna play a game?

15/10 is enough, but there are pairing problems. (U getting paired by someone 200+ points higher than u). 

I actually prefer to move it forward rather than away (4. Ne5).

18. Nc7+ is done one move too early.

18. g3 first and things might look better.