So, you care about your sister, but you can't talk with her because she'll be mean to you when you talk to her. Can you either email her or give her a note? The reason why I suggest those two things is because she can't really interrupt a note with anger. And, in that note, what I think you want to make very clear is that #1 You care for her, #2 Ask her whether she could tell you why she hurts herself when she feels comfortable talking about it. Let her know that you'll be available to support her whenever she needs it. #3 If she won't talk with you, ask her to either talk to someone that she trusts or find a group that will support her. And, of course, emphasize that this is all coming from a place that you want her to stay safe. If I'm saying anything that's inaccurate for you, feel free to modify what I'm saying.
Now, in terms of how you can stop worrying about her, at the end of the day, all you can do is say your peace. You can't even force your help on her because that might irritate her. At the end of the day, she will do what she wants to, but you can at least let her know that you'll be there when she needs you. You're trying to understand where she's coming from in terms of harming herself because you care and you want to help. After you do what you can, you just need to step back and give her some space. That doesn't mean stop checking on her, but just give her some breathing room and just check in with her periodically.
Alright. I hope these ideas help. Good luck.