Sorry if this post turns out to be long.
I agree with other posters that the shaking is probably stimming. Is it like the way that other people 'bounce' their leg up and down when they're nervous? If so, I do the same thing, especially in times of stress or increased anxiety, which it sounds like you are definitely experiencing. Stimming is something you need to do to relieve stress; if you can't do it, you might have a meltdown which will be much more embarrassing for your grandmother.
The headphones and the bear are hiding mechanisms. I understand it, I have a bear (it's a dog, actually) that brings me comfort and that I would carry around everywhere if I could. Autistic people commonly use things like headphones and sunglasses to help shield them from sensory input that is often too loud and too bright. It's perfectly understandable, and is often necessary. The bear is more complicated. It isn't really appropriate for someone of high school age to take a bear with them everywhere. Can you keep it on your bed and take comfort knowing it's there? (That's what I do with my dog. I only take him out when I really, really need him and when I can be alone..) Or can you get a keychain that looks like your bear that you can carry around instead? Something small that won't be noticed?
It sounds to me like your grandmother is being a little bit selfish. Her insistence that you are faking is her way of being in denial. She doesn't want to believe that you have a real problem. She's also probably embarrassed by it because other people can see it. She's worried about what other people think, which is something she's eventually just going to have to get over. I think that you might have to just tolerate her behavior for now. Don't try to convince her, you won't be able to. She needs to be ready to see the truth on her own. Right now, she can't face it, which is why she keeps denying that it is real. I know it's hurtful to you for her to say you're faking, but if you can, hold out for a little while. It'll probably be a few years before she starts to come around.
_________________
You don't need to hide, my friend, for I am just like you.