Advice for autistic teen who overthinks and then spirals

Thanks so much for your comments. Very timely as, despite me having to collect her from school because she was so distraught, she did gather herself this afternoon and went to the gym with her Dad. BUT she has just messaged me to say her friend has TOTALLY cancelled and - as when she was at school - she is upset and wants to come home. I need to have a conversation with her when she gets home to avoid ANOTHER sleepless night and ruined school day, so your advice is very helpful. Thanks.

She will need to know that in non-autistic social groups, flexible planning isn't intentionally cruel. I think A Field Guide to Earthlings has a section on this. 

According to Jung, most will experience a feeling of being too connected, too much like everyone else. It's part of the Jungian Mask and the internal experience of what is now termed "NeuroTypical". It is a polar opposite experience to being Autistic and often feeling disconnected, isolated or even marginalised for even trying to fit in. This is where the Double Empathy Problem comes from - a majority who might be stuck in a particular bias, prohibiting the ability to ask why someone is a little bit 'odd' or different and not intuitively social. 

This is completely normal autistic expression. Are the downward 'spirals' always related (in some capacity) to social and social-interpersonal struggles?

Smash cut edits, sudden unplanned transitions will cause distress. You can help her learn to manage what she Expects from others. If one friend is consistently inconsistent, learn to expect and make room for that or don't make plans with them if you can remember. As we get 'stuck in the moment' - Right Brain thinking, and already have trouble with Left brain planning/executive function, creating new conscious habits are really difficult. 

This is partly due to what the Bayesian Theory describes as a difficult predicting social patterns. It is not 'Sameness' we need exactly, this is a surface quality which can be easier than the underlying principle of Dependability. 

The second Autistic difference that is completely normal is being far more intensely impacted, so feeling deflated or let down feels like the world is definitely over. My father and I are always LOL-ing hysterically at Marvin (hitchhikers guide) who makes Eyesore look like a day in the park. Because the internal experience can be that extreme. The other thing to note is that it can feel like we are always invaded, always vulnerable and this is because we're not filtering out incoming signals the same, so it is incredibly difficult to learn external habits of creating health boundaries with others. 

What she can use is probably a good few books on how the world should work, and how it actually does work. Sometimes the best idea can be to sit in a bookstore and see what books on the nature of being human, the self-help section, the psychology section she might find of interest. The only way out is through. And the better we understand the social world around in contrast to our own differences (the intense impact, severe difficulty with transitions), the more prepared we'll be for what we encounter.

I recommend the resources from https://dialecticalbehaviortherapy.com, it can be more effective than CBT for people with autism, the radical acceptance worksheet really helped me. 
What activities does she find regulating? She might benefit from some sensory items like a weighted blanket or spending time with animals (if she likes animals)- planning regulating things and doing them regularly even if she ‘feels fine’ can help build coping skills.