You're both right, it wouldn't be fair for both parties to restrict each other's nature.
I don't know what go into me, I guess It's been a difficult phase. Not so difficult as it was when I didn't know about my asexuality of course. But now I see limits everywhere, although I already felt them but never really thought they existed...and now..well, I'm lost.
I'll follow your advice and look into asexual sites to find people like me.
And about the girl in question, I'll just keep being the person I am with her and shove feelings aside.