There is this girl which i got randomly hooked up with by a friend, didn't quite like her at first, but later the attraction kept on building on. We got drunk the night we were introduced and had sex at my place (She was my first). After a week she texted me, that she wants to meet up and pay for the mess she made (nausea after alcohol consumption). Then some the conversations continued and it was fun and interesting for both. We haven't had sex afterwards. Later I started to see, that she was making too much kino and attraction to a good friend of mine (I wanted to throw her to this guy that night, but the situation worked out that I was with her). A week later she got drunk and said that she likes him and that sex between us is never gonna happen. She stayed at my place and in the morning we had some talk. I explained that, this kind of situation doesn't work for me and that I need to think whether I want to continue meeting up with her. She said that she gets it and that there is no reason now to see each other, so we left on that note. Yesterday I was playing guitar in a pub and she walked in (she knew i was playing there) just sat, smoked and walked away after a while. In the morning I found a letter on facebook, that said our situation really bothers her. Stated that we are just friends, that she feels when she is being seen as a sex doll (yeah, after one time). Asked some questions in the letter, which I haven't answered yet.
So guys, need some advice. I like her, she really is fun and the 2 months of our (idk how to call it, but lets say relationship) much crazy stuff has happened and I would like to keep her (in more that just friends way). Would appreciate any material, personal suggestions. Will add any detail if needed. Thanks!

Be honest and tell her the truth. She's not just a sex doll. You like her and it's hard for you to play the 'just friends' game. Tell her to chose between starting something more than friends or keeping her distance while you get over her.

It sounds like she wants to keep pretending to be friends while getting that special kind of attention. And trust me, that kind of attention is addictive to women. Even if guys don't pay for my dinners or take me out on dates, if they're interested I can feel it and the addiction is to that 'vibe' they give off.

Read some topics and tried the freeze out. At first she was very confused about what was happening. We met a couple of times at local bars, i was quite cold to her. Then I asked her out for a little chat, she was willing to talk about a time, when we were at a friends place, where she pretty much was hitting up on some of my friends (even laying with one in bed in quite a sexy pose). I didn't show any anger, but after that evening I was cold to her. I didn't speak about that evening with her, but said that everything is just fine. After a few days I chatted her up with intentions to meet her, but she said if our next meeting is going to be as cold as the last one, then she does not want to maintain such communication. Haven't chatted her up, but I know, that she was discussing me with one my friends (through messages), she told me, that she likes him. She called me resentful.

To me the freeze out went as expected, but I really don't feel what to do next. Thinking about freezing out for another week.

You seem to want a relationship with her. The only way that is going to happen is for you to take her out somewhere, to the park, anywhere, sit down with her, and explain this to her. Tell her that she's more than a sex doll to you and you want her to be your g/f (if that's what you want).

Just be direct with it.

Along with this obviously means she no longer can flaunt herself to your buddies around you and lay in their beds etc. Like the other poster said she is addicted to the attention.