The most likely reason they would not have told her is if she didn't ask. The name of a diagnosis is not going to change what they do to help her so if she didn't ask they may not tell her because the label may only make her feel worse.

Or she knows but doesn't want to say because she thinks people will look down on her for it. In regard as to why she's acting cold, I'm not sure but it could be many reasons. Maybe she's being cold because she's afraid of getting involved. Or it has to do with the not dating recommendation.

Its hard when someone is in a place where you feel like they are being manipulated. My question for you is what other options does she have right now? Since she doesn't seem to want a relationship with you for the moment where else might she live that would be a healthier enviroment. She may feel trapped with them and have no better options. If you think she would be better somewhere else you may have to figure out where else she could stay.