As someone who also has visual and auditory hallucinations, they're not the most fun nor pleasent experience (however, I don't cut so cant help there). I'm assuming the hospitalization would be to get her to stop cutting or give her alternative copings ways and start her up on some antipsychotics (which tend to have some unpleasent effects).

There's also outpatient therapy both for medication and talking, so you could also try that.

But, to answer your questions. How do you know she'll get the right treatment? Well, as someone whose taken a course in medical pharmacology and plenty of biology (and currently a human anatomy and physiology course), it's basically a guessing game. They have the meds available but to know which ones will work and how well really is a trial-and-error test. Obviously there's the stats on how good certain meds are but it's a guessing game if your daughter will react positively or not to the meds. However, once it is found, then it is quite effective.

How do you know long-term is right? For starters, she probably won't have access to things to cut with, and can get some proper treatment, as well as a diagnosis if she doesn't have one already. The long-term would probably refer her later to outpatient therapy, or if they have therapy in the long-term, finding out her possible reasons for cutting and tackling them.