My best friend is making me uncomfortable?

As weird as this may sound, lately our friendship has been more like a relationship. I mean she doesn't like me romantically, but some of the things she gets annoyed with me about are weird. The other day we were hanging out with another one of our friends. She was getting mad at me for not giving her enough attention. Apparently I was laughing more at what my other friend was saying than what she was saying. She felt like she was competing with our other friend & she felt like I liked her more because she's prettier. She was also annoyed when she found out that our other friend was spending the night because she wanted to have alone time with me. I mean I understand wanting to have quality time together or whatever, but every other time we hang out it's just us. I don't understand what the big deal is hanging out with a third person.

Basically, this girl is very insecure. She is overweight, self harms & lives in an abusive household. She has a ton of medical issues. She thinks of me as her only friend & if anything was to happen to our friendship she would kill herself. It puts me in a very horrible position that I don't want to be in.

What do I do? It's not like I don't want anything to do with her, but I feel like this friendship is very unhealthy.