It kind of blows my mind that, if they had no beds or whatever, they didn't have some information as to an alternative. I don't really know what to say except start a long-winded tirade against The System. But I've been doing it a lot lately and it won't help you.
I would find some kind of medical crisis line, suicide prevention line, whatever, and just start from there. Some of those people are trained to have information on resources and hopefully they would be able to help you out. I feel for you and I will be thinking of you and your sister.