@Fish and Chips: Pardon me writing a novel here, but, it sounds like this girl isn't getting the help she needs. Maybe it's not accessible to her or maybe it's because she doesn't understand how to get that help or how to get better or how to self-manage, etc. If she has a psychologist, maybe she's having a hard time identifying what would help her, so maybe she and her worker don't understand each other well. But based on how she talks to you, it maybe sounds like she's trying to get attention in lieu of that help. Looking for sympathy is sometimes easier than struggling through the steps to managing a mental illness in your day-to-day life. But none of that means you are obliged to sacrifice your own sense of security to accommodate her special needs. As much as it's important for friends to make compromises for each other's happiness and consideration, you are not trained to handle whatever she's dealing with, and it is incredibly risky, for both you and her, to assume that responsibility. You shouldn't be considered less of a person just because you want to preserve your own comfort.
This might sound harsh, but if she treats you like you're not a "true friend" just because you don't want to handle a problem that you are not even trained to handle- screw her. You have the right to step back if you feel that you can't help and it's making you uncomfortable. You are under no obligation to manage her issues for her, and you have the right to preserve your own mental health. I don't know the semantics of this girl's disability or disorder, and I won't pry, but she too has the right to live with the social liberties of any other person - but to a certain extent, she is still responsible for herself, and trying to make herself the centre of attention by shocking friends and loved ones with her issues is not only generally "dickish", but it's also VERY irresponsible and risky of her. She is making her issues your business and problem, but not providing you with the information necessary regarding how to handle her disability and limitations related to it.
We as people often hesitate to defend and preserve ourselves because we don't want to look or feel like "the bad guy". Girls especially. We don't like doing things if we're worried that we'll seem rude or like a "bitch". You don't have to ream her out, but if you want to stand up to her, let her know that you are not qualified to handle these situations, and it puts you both at risk if she is expecting anyone but professional help to do so.