Was your intent to die? Because as an adult I will say I have never been hospitalized for self harm alone. Only when coupled with suicidal thoughts. I tend to use it as a test to see if I can trust my therapist/pdoc, and my current ones never recommended hospitalization based on that.

When I was a teen, sure, all the time. But not as an adult. So don't worry too much. Unless it was really severe and they fear for your safety they probably won't force inpatient. Recommend, maybe, but no force involuntary.