it might help to explain to her what would happen if she agreed to see a GP
teens often have very strange ideas of what happens if you are diagnosed with some kind of mental health problem
first of all, the GP isn't going to anything very drastic at all
they will have a brief chat to establish whether they think she needs to see somebody more qualified (CAHMS)
if they decide she needs help, they will refer her on; waiting lists are long at the moment so this may take some time
when she gets to see the specialist, they will not do anything sudden or nasty or without her consent either
it will start with a longer session to find out what the problem is- at some point they will probably ask you to leave the room so she can talk more freely
the treatment will probably focus on identifying situations that are difficult for her and teaching her techniques for dealing with them (CBT)
this may involve relaxation techniques, techniques for avoiding or rephrasing negative thoughts, techniques for handling difficult situations
it is not about taking away her control, it is about putting her in control of her life
my dd was referred at about this age
in her case, her MH problems did turn out to be part of a longer problem (started much earlier than your dd's too) and she did need medication in the ends, as well as the CBT
but she is now a functioning adult, lives away from home and is studying the subject she has always dreamt of
hang in there- and hope your dd gets help soon!