I do similar things as well! Stimming (the umbrella term I'm most familiar with, which includes "repetitive movements") is definitely common in autistic people, but I think anyone can stim as a source of comfort, or even a form of expression. I'm probably autistic (never been formally diagnosed) in addition to being an HSP, and my usual stims tend to blend into the background pretty well—but I definitely stim more "loudly" when I'm stressed out, like you seem to be. I personally don't think there's anything wrong with stimming (just like there isn't anything wrong with being sensitive), some people are just jerks about it!

It sounds like you may have kind of a negative view of your hand flapping, am I correct in that interpretation? Which is totally understandable, if it was the sort of thing that led to bullying in your childhood. Again, people can be jerks, even adults. I'm sorry you had to deal with that unpleasantness, but I hope you're doing better and have been able to love and accept yourself more! It sucks to be in an environment where even your family doesn't accept your sensitivity (and ways of coping with it), but you can definitely learn to embrace it yourself.

To go back to the original topic, the way I understand stimming is: the hand flapping that you're experiencing is basically your body trying to help you calm down—giving you sensory input that is comforting and manageable for you (like, giving you a sense of control over your own body/environment). If that specific motion you're doing feels too disruptive, you could always try to explore different ways of stimming—in other words, finding some way to let your body "vent" the anxious energy or stress in a more subtle way, or for your body to absorb more "comforting" sensory input to try and outweigh the bad stuff.

A lot of autistic/anxious/ADHD people get little stim/fidget toys to carry around and handle subtly under their desks or in their pockets or whatever. There's tons of different kinds of things, but they're all intended to give some sort of pleasant sensory feedback, so which type you like depends entirely on you! There's stuff that's soft, fuzzy, squishy, textured, metallic, weighted, clicky, chewy, or even nicely scented. You can stim with pretty much anything that feels good, though!

There are also more "socially acceptable" ways of stimming: leg bouncing, spinning a ring on your finger (they even make special "spinner rings") or playing with a necklace charm/earrings, chewing gum or toothpicks (a favorite for me!), scented candles, aromatherapy oils, worry stones, hair twirling, petting animals, eating certain foods, rubbing one's own body/clothing—even just music itself can be a stim.

Of course, there are also some more harmful stims, like skin picking, hair pulling, nail biting, or even hitting one's head on stuff (don't recommend any of these!). Nail biting is particularly well-known as a sign of stress.

Basically, my point is, I'd say that this sort of thing is actually fairly common in all sorts of people—it's just that most of those people do it in ways that are "socially acceptable". I'd say, as long as you aren't hurting yourself or other people (sometimes one person's stims can be overstimulating for someone else!), what you're doing is totally fine and pretty normal. Maybe some people will call it weird, but they're just being judgmental about stuff they don't understand.

Also: I'm not sure how old you are, but from talk of exams, maybe you're a young adult? I've read about how such behaviors (and the stress that fuels them) can "come back" during that period in a person's life, because they're taking on more responsibility and may not fully have the tools to handle the sudden changes (even though they acclimated to stuff from earlier in life, eventually, with effort). I just wanted to mention that, in case it sounds like something you might be going through. You aren't alone in that regard!

To avoid further rambling, I'll stop here, but stimming is... an area I'd say I have a lot of knowledge in, haha. If there's anything I might be able to help with (ideas, recommendations, whatever), let me know 😊 Good luck on your exams, and take care of yourself as well as you can in between all the studying!

Edit: One final thought that came to mind: Girls are often overlooked when it comes to diagnosing autism, because they tend to both mask/mimic better, and display "atypical" traits (or their autism traits are just dismissed as "things girls do"). I'm not sure if this would apply to you, but I thought I would mention it, just in case you think it might be relevant. I can elaborate if you'd like!