Hi miss_rainy. I think if you are diagnosed as autistic this could definitely be part of autism.

But another way to look at it is you seemed overwhelmed with emotions you did not know how to express and so you shook hands and fingers and that helped you cope. That is a valid coping mechanism especially when your parents are passing anger into the home.

Here is more of symptoms of autism that do list shaking the body to cope
Autism Spectrum Disorder Symptoms | Psych Central