Were we tactically wrong to draw this game?

My goal was to attack the weak black d pawn or get his light bishop for my knight and he wouldn't budge with his queen or trade material, he already has that nice f pawn and castled when I'm not ready to castle. Did I play that right or wrong to make a draw?

White was completely losing this game. All along black had a huge advantage because white made a few strange choices. I do not understand black´s choice of accepting a draw.

14. Bb6 Bh4!
What do you suppose you do against this?

And at move 13...f4? 13...fxe4!.

But black didn't seize these opportunities.

After 14 Bb6 Bh4 I think he is losing some material to g3 as both his queen and bishop are threatened by smaller pieces at the same time. He may have some sort of attack after that but I think I'd be better off than him.

As far as Fxe4 I think that may have been arguably stronger for him opening that file up, but how would he follow up with an attack after that?

Alright first 14...Bh4:

It's not just arguably stronger. It loses material for white. You see?
A mistake was made with the moves Be3 and Nc5 which got you into trouble. Sorry if I'm being a bit too blunt, not my intention.

So I was smart to draw then

Well that depends on perspective. Black didn't had to repeat his moves. So if he made the correct move after Bb6 you could have lost the game.

After 15.Qd8 you are pretty equal actually. He doesn't have his attack anymore and you could have played further if you wanted too.

Your game was full of instructive mistakes, please look through the variations :)