How Do I get my ex girlfriend back?

hello. I am new and made this account just so I could ask this..

This is my first serious relationship and here's the situation... This girl I've been dating for one year (long distance) let me know a few days ago that she wants to break up. The reason being, she's been going through emotional issues (trust me, there is alot) and she wants to clear everything out of her life to get a new start. Now, the problem is.. SHE WANTS TO BE FRIEND! She calls me everyday ever since the break up, we talk normally and she says she still loves me. In fact she never actually broke up with me herself. She FORCE ME to say the words to break up with her which made her throw up later. She says she couldn't bare saying them because it would hurt her too much.

She now offers to pay for my hotel room and everything so I can come see her in a few weeks. Clearly she is not ready to break up. How do I make her see she is making a mistake?? Do I stop talking to her to make her miss me or be her friend to show her she needs me in her life?? Any suggestions??? PLZ...