Girlfriend wont stop cutting herself

 As the title says, girlfriend wont stop cutting herself. I, (16M) and her, (16F) have been together for almost 5 months and she has a history of depression, anxiety, and SH. I knew this going into the relationship and helped her through some problems with her depression and anxiety in the first two months. I don’t know how long she was clean for but she started cutting again in January. In January I had a talk with her about how it worried me and how much she means to me and that while I want her to eventually stop I understand that it’ll be very hard and I’m okay if she relapsed a little on her way to being clean.

Well fast forward now and it’s even worse. In January and early February she told me the reason for her doing it was her mom’s overbearing mess in her life. I understood that as a reason (extreme reason but still) to SH. Now, however, she is telling me that she is just doing it to do it. I tell her how much it worries me that she does it but she doesn’t listen and just tells me not to worry about it. I also suggest that she gets help or tried another coping method but she won’t listen to that either. She said she will continue to SH no matter what I say. As of right now I am thinking of giving her an ultimatum (extreme, I know). The ultimatum being that if she doesn’t stop cutting by a certain date (idk maybe a month?) then I’m going to end the relationship. I can’t keep going to bed every night worrying if she is cutting while I’m sleeping. What do you think I should do?

EDIT: she is and has been seeing a psychiatrist for months now but she refuses to open up to him and doesn’t even let him know about her SH tendencies.