She said I am her boyfriend but I have never successfully dated her

I met this girl on FB last April, she was the ex of a very good friend of mine long time ago. She was chronically ill, needed long term medical care. She got a boyfriend at that time, but they got some problems and he didn't show enough caring for her. We started to text and chat on phone a lot, and I slowly got attracted by her fun loving personality.

Then by the end of last summer, she broke up with that guy. And we spent crazily long hours chatting everyday, and even got really intimate on phone (um.. you get it). Yet the problem is, everything happens only on phone and whatsapp. Of course I asked her out a lot, she refused every time. Then in September 2014, she went overseas for medical treatment. She stayed there for a few months. During that period we kept phoning and texting each other a lot, and exchange birthday and Christmas gifts. She once said I am her boyfriend when she is texting someone else, and showed me the print-screen of that message somehow. She also make me a scarf and sent me a love letter for Valentine last month. And last month she was back. I have asked her out for a few times since then, she refused.

I am really confused. On one hand we get really intimate (well, on phone and texting), and sent each other stuffs like love letters and valentine presents, but on the other hand I have NEVER met her in person, not even ONCE..

I know the medication that she has to take and her illness sometimes make her really tired and lost interest in things. I don't know if that's the reason why she refused to meet me. I really, really want to meet her in person. But when I kept trying to date her, she kept refusing. What is this all about.. please give me some advice. Many thanks..