White could have won the game...White king can escape the check and should have tried with three pawns against two of the black... Moreover the one white pawn is two moves away from becoming queen

I don't think it was a continous check situation, in hindsight - I haven't looked too closely but I do think that you could have set up some tactics to win a pawn or two once I escaped check. I would have then been able to move my queen offensively, though. Either way, you had the initiative by queening first and I thought a draw was probably a good agreement. Plus, honestly, I thought you had a won position after about 25-27 moves, so I was actually quite content with the draw, even if it wasn't the right choice.

 I'll be interested to read the comments!  :)