

I don’t have advice but that does just sound like being 13. It’s a rough time. If you can see, or if she asks for, something actionable that would help (like “my homework is really stressing me out, can you help me”) by all means do it. But for me I think I just learnt coping mechanisms the hard way as I grew up. Most people change a lot in the ensuing years after 13, usually for the better. I’m sorry your sister is going through that.
One thing that does come to mind is to check if there’s any external issues that are causing her to feel so bad. There often are. You might be able to learn something by talking to her more?
Bucket of cold water, stick your feet into it.
Tin foil in the windows to reflect radiation.
Cold tap over inside of forearms and wrists (iirc ears work well too, but of course a more awkward reach if you’re just using a bathroom tap).