MenoMum4 why do you describe your child as "possibly the most beautiful little girl ever"? What has this got to do with anything?
What you say suggests your DC is reacting against gender stereotypes. This is common among teenagers and super common for those who are lesbian or gay.
There are plenty of accounts that lesbians in particular take many years to come to terms with their sexual orientation. It doesn't help that there are no butch lesbian role models. Indeed being a butch lesbian is deeply unfashionable.
In contrast, coming out as trans at school gets a girl lots of attention and extra status. But once you've told everyone you're trans, backing out - changing your mind - can be very tricky.
Be grateful for the delay in seeing the clinic. Putting your child on medication is not going to help and is likely to make matters worse. Your child will never be a man.
Gender non conforming girls need support to be the gender non conforming girls they are rather than encouraging them to enter the medical route.
Sex changes are impossible and medical transition for girls is very destructive of their healthy bodies. Even teenagers who act as if they know all about trans issues are unrealistic about what can and cannot be done in terms of physical changes.
I've heard from a teacher that kids think you can have sex change surgery. Not surprising, as many adults believe the same
You might find the group 4th Wave Now helpful. It describes itself as:
A community of parents & others concerned about the medicalization of gender-atypical youth and rapid-onset gender dysphoria (ROGD)