Just to add, the reason I think this is because she seems to have found almost all of the personality traits in herself. This is uncommon, people usually have some but not all.
@Proudgypsy, I agree that there seems to be something of a trend/social contagion thing going on at the moment, with some teens and young adults in certain (especially online) communities self-diagnosing as neurodiverse based on possibly inaccurate understanding of the conditions and somewhat distorted self-representation, combined with the teenage need to belong. But I'm not sure that I see what you see in the OP's description — it doesn't seem overtly like a methodical ticking-off of stereotypical traits to me, though I could be wrong.
And when you say people usually have some but not all of the "personality traits", I agree that autistic people may present more obviously on one criterion than another, and will have some of the common characteristics and not others. But when it comes to core or very common traits, you sometimes find that when an autistic person doesn't apparently display that, they might have some other particular unusual difference that's essentially a disguised version of the same thing, or expressing in a different and perhaps hidden way.
I agree with your note of caution, and think that if it is the case that the DD has got caught up in an unhelpful idea, there's a risk the outcome of an assessment will cause difficulties either way. Either she gets a (mis)diagnosis of ASD/ADHD, resulting in inaccurate medical records, maybe unnecessary medication, and a label that may be difficult to lose later on. Or doesn't receive a diagnosis, which could be upsetting and unbalancing, or lead to a campaign to prove them wrong in some way. On the other hand, if she's mistaken about having ASD/ADHD and doesn't seek assessment, she'll continue on under the impression she has these significant neurodevelopmental disorders, possibly seeking adaptations and adjustments that may not help her.
But if she actually does have ASD and/or ADHD, then being disbelieved by family could be damaging. And most of the time, IMO, being properly assessed and (hopefully) correctly diagnosed can be incredibly helpful for people with these conditions. To me, there's enough in OP's description to suggest that it's possible she has a neurodevelopmental condition, and given the extremely high rates of mental illness, under-employment, suicidal ideation and suicide, and other life-damaging difficulties autistic people face, I'd err on the side of encouraging a thorough, credible assessment.