IMO, it doesn't sound like a relationship, since it was only a month....it sounds more like you developed a deep deep infatuation with her...much more than she did with you...which was probably very flattering for her. Perhaps once you had sex she realized that you were much more invested emotionally in this than she was, and decided to end things before you got in too deep, not knowing that you were already in.
Once it ended, you soundl like you've become obsessed...and as someone who has major obsessive thoughts...I feel your pain. I've done the same thing. But I agree with the others that you have to move on. Find someone that wants to be with you, don't pine away after someone who doesn't want you. you deserve better than that.