really sorry to hear you are going through this, OP
agree with everything adoptmama said
I'd get back to the GP and explain that there is a real risk of suicide
I would also ring the school and explain what is going on and ask for the support of the SENCO/pastoral support officer
when my dd started self harming, the school put pressure on the NHS to speed up her CAHMS referral
dd's problems were physical disability and chronic pain rather than anything affecting her learning, but they led to the same hopelessness
she also attempted suicide
CAHMS were brilliant: they worked with her and helped her to see that though her condition was given, the way she dealt with it was not
she had pretty well dropped out of secondary when the treatment started
three years later, she is at sixth form college, loving every moment of it, and confidently looking forward to the day she leaves home to start the next step of her life
nobody could have believed two years ago that this would happen
so keep pushing- get help for your dd, try all avenues