I told one or two of my friends that I had times of wanting to "hurt myself". One asked for more details, the other didn't, but both said to call them if I ever felt like that again and they would talk to me till I felt safe again. YOu could say you are scared of lots of people finding out but perhaps offer her a safe older person to tell (I'm guessing she might need that support herself) if you want to. I'm not sure I would want to tell a friend and insist they kept it a secret.
Or could you just call your friend anyway if you feel like SI again and just tell her you are scared and need to talk without telling her what you want to do?
The last time I felt like SI I called a help line where there were counsellors. The counsellor I soke to was really good and when I mentioned that I had a "safe place" to imagine but couldn't get there, she asked me lots of questions about it until I was able to picture it.
Hope this helps.
Hugs if you will have them
Caroline