I understand how this causes you discomfort, HurrySpring. It just shows that you have feelings for Betsy and really care. That part is a good thing. I get how and why it's difficult to support someone we have a special connection with without being too drawn in... I struggle with this sometimes even though I actually had some professional training for it: how to deal with people's problems compassionately without my own feelings becoming detrimental either on the relationship or on myself. But friendship is not a relationship between a doctor and patient, or something like that, and we typically don't want to limit our feelings. It is sometimes necessary for the sake of our own well-being though. I don't tend to be too open about letting people in my home, but I definitely have difficulties with getting into people too much and setting mental boundaries.
Definitely do not open your house to an active addict, however you like her. I agree with others, listen to your instinct. Maybe try to help find accommodation for her? Like a shelter or something? I think letting her in might just make her state worse... because then she would not need to make efforts to resolve her situation.