@cheshirecat2913 I knew your DD was going to be ND, it stood out a mile from your description of low self-esteem and her fixation with this girl.
Teen years are bloody hard for anyone but they can be excruciating for ND teens. Self-harm and self-esteem issues are sadly really common so it's good that you've got a heads-up on this.
Your DD sounds fixated on this girl and her achievements, and she also sounds quite demand-avoidant, plus the usual black-and-white thinking.
As an autistic/ADHD woman myself, I know if I believe a professional (in any industry) isn't up to scratch, then I'm not willing to waste my time. That sounds a lot like your daughter.
The problem is that many of us ND folk tend to make up our minds quite firmly, and it's difficult to change it. When you throw in the immaturity of the teen years and the typical teen belief that they know more than the adults, it's a tricky combination.
Allowing your child to feel as if they are in control can be useful. Could you come up with a list of private counsellors/pschologists with experience in autism/ADHD and asking your DD to pick one? Standard CBT often is of limited use with ND folk, so experience with neurodivergence is vital. I have heard that DBT can help but I don't know much about it.
ND can sometimes create an all or nothing mentality, where if you can't be the absolute best, it can feel like it's not worth the effort. That's not a healthy mindset but it can often be the default.
Sometimes it's because ND people spend their lives feeling like an imposter, an outsider, and not quite as good as everyone else. So when someone is CLEARLY much better than you, especially in areas you're passionate about, it can be yet more "proof" that you're just not good enough.
Self esteem is at the core of this issue. Ideally you'd remove your DD from any environment with this girl because distraction can be key. But it doesn't sound as if you have that option?
Does your DD have access to fellow ND teens? Joining a group might be really helpful.
Also, have you considered what kind of language you use about yourself? Are you critical of yourself? Do you celebrate your own victories and uniqueness? Our DC often pick up attitudes from us, and having the attitude that actually you're pretty magnificent can help her to absorb the message. It's hard to describe in writing, it's not about being arrogant, it's about loving yourself for who you are, and celebrating your own uniqueness.
Directing your DD's gaze to a new fixation might be the answer while simultaneously boosting her self-esteem. Can you think of any ways that you can do this that would be meaningful to her? If she's obsessing/uber-fixated on a shiny new subject, she might be less interested in beating this other girl.