Can a doctor send you to a psych ward or anything similar for having self harm cuts?

I'm not sure she will even notice the cuts, most on them are in non-visible areas. I do have 1 on my arm but it's not obviously self harm IMO. Basically, I'm only fucked if I end up needing a pelvic exam, which I might.

Although, I would kind of like to tell her about the cutting and some other things I'm dealing with, just for the sake of talking to someone. Also, I kind of wish someone would notice the cuts, just because I want people to see how much pain I'm in, and ask if I'm doing okay.

I do have a therapy appointment tomorrow as well, but I'm scared about how it will go, and I'm not sure if I'm going to tell the therapist about the self harm or not - this is my first appointment with her. She's a really new therapist, fresh out of grad school, just got certified in August, so I'm not sure she'll handle it right. I've heard a lot of stories about therapists reporting self harm or suicidal thoughts even if they aren't life threatening, and I'm scared it will happen to me.

Edit: For context I'm 19. Also, the cuts are all cat scrathes.

Any advice or thoughts are appreciated 💜