No question that if she is cutting, she needs some kind of help. As for the hospital, that really depends. If she is truly suicidal, then definitely yes, but if not, the hospital is not going to be much help.
For most people, in my experience, the hospital is a very short term crisis stabilization. They start people on meds, connect them with people for continuing care, and send them home. If those services can be provided outpatient, it's a lot less restrictive.