It very much seems like she was lonely when she went out with you. Or she could have thought that you have great qualities but there wasn't much attraction there. It could be one of a million different things, I don't know. But what I do know is that she doesn't want to be with you.
She didn't want to be in a relationship with you but wanted to be friends with benefits. Which seems to back up the idea that she was just lonely two months ago. Once again I can't know for certain because I wasn't there, just an idea.
The problem with open relationships or friends with benefits is that typically one person develops feelings while they other doesn't. One person usually ends up getting hurt badly in the end.
My take on those situations is that you should be with someone who wants to be with you. Be with someone that LOVES to call you her boyfriend, loves being with you and happy to be dating you. If the person doesn't share the same enthusiasm that you have for them then the relationship won't last long. It's best to move on and find someone who will.
My suggestion would be to put some distance between you and her for a while or at least until you are no longer in love with her. If you continue to be around her those love feelings will persist. You will only end up feeling more pain and frustration.
Check this article out for falling out of love with her:
Quick exercises to get over an ex