Hi, my DD is in the same situation. Putting so much pressure on herself and won't really talk to me.
Luckily, she is under CAMHS atm. She cut herself at the weekend (only the second time) and was sent home from school today. She wants to be there (in Y12) as she says she won't achieve anything without being there, yet seems to be petrified about actually starting any work at home!
A counsellor, not her normal one, visited her this pm. I was there, too. The counsellor told her many ways of distracting herself from her horrible thoughts.
One was to wear a rubber/elastic band on her wrist and ping it so that it hurts! This evidently distracts from your thoughts.
Another was "switching" where you absolutely concentrate on a sound in the environment around you, eg a ticking clock, the traffic outside, bird sounds, etc. Or you could notice your breath - yes, I can cope with this for another breath and another...
What would I say to a friend who came to me with this problem? She (your DD) wouldn't say, "you really are rubbish, etc" would she? She needs to be kinder to herself.
DD was quite rude to me today, which is pretty unusual. I did cry a few tears in front of her as I wanted her to know how much she hurt me! My feelings can be hurt, too, not just hers.
Have you tried to get her to talk to The Samaritans. DD has talked to them a couple of times. They were very helpful.
I said to DD this (her situation) is not insurmountable. In the scheme of things, it's really a very small percentage of her life. She doesn't need to think these horrible thoughts and project into a horrible future. It's easier said than done, I think
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Wishing you luck and fortitude!