I have a lot of autistic traits but don't have a diagnosis. Maybe I'm a little bit too, but then we're not supposed to say that. Everyone's different. I can recognise faces - although I get confused about who's who in films sometimes!
Not wanting to be touched is typical of autism. Social anxiety is typical of autism. Having difficulty expressing yourself is typical of autism, and they might think your quietness is an expression of that. I can see why they might think you're autistic.
I guess they are trying to help. If you can talk, and you think it's lack of talking that's leading to the diagnosis, why not speak up and tell them that? Over and over until they listen. Show them they're wrong.
Or maybe, consider that they might have a point - because autism is a spectrum and lots of admirable and highly intelligent people have it/had it. Einstein, Elon Musk, Alan Turing who broke the Enigma code so we won WWII. No one else could do these things without that level of autistic focus. It's not a bad thing. Not always anyway.
If you think they're wrong though, challenge them - but not in a way that looks like an autistic meltdown. 🙂
I hope getting your feelings out has helped and you find a resolution. It must be frustrating if your mum is suffocating you. Again, why not talk to her about how suffocated you feel, if you can talk. It will show her that you *can* talk and don't have the same level of problems that she thinks you do.