So I didn’t have this exact issue growing up, but we moved often for my dad’s job and I changed schools on average every 1.8 years. (Can you tell I’ve done the math?) I was also shy, quiet, and unsure of myself. My anxiety ran very deep and would get pretty bad at the height of transitions. I’d not say I got bullied, but I do remember one school in particular where my classmates felt particularly mean. Typically, I’d finally start to feel settled by the time we moved again. Rinse, repeat. You’d think I’d have gotten good at making new friends at some point along the way, but no. I was not. When I had to change high schools with less than two years to go, I gave up and decided all I’d do was put my head down until it was time for college. By the time I got to college, I refused to study abroad because I wanted four years all in one place.
Anyway, I don’t think changing schools again is the answer. It sounds like your parents are somewhat in the loop since they must’ve been involved in the school changing process. Can you tell them you’d like to speak to a therapist? It sounds like you have a lot to work on, like anxiety and confidence. You could also ask to speak to your school’s counselor.
Being new — especially if you are coming in later than everyone else — is really hard. But the beginning is the worst part. If kids aren’t talking to you on day one or two, that’s not a reflection on you. I don’t think anyone is judging you. I don’t mean this as a slight, but I doubt anyone has noticed you yet, especially if you’re keeping to yourself. Something I wish I’d done when I was brand new in HS at 17 is say to someone who seemed nice in one of my classes, “Hi, I’m Copa. I’m new.” It’s so simple but it never even occurred to me back then. If you’re feeling brave, try it… especially if you see someone who is also by themselves. You say you’re into science. Is there some kind of science-related club you can join? I always did better in smaller, more casual group situations, especially if I knew we already had a shared interest.
Good luck. If it gives you any amount of hope, I’m now a very friendly adult! Who is confident! I can talk to anyone. I’ve moved around to new cities a bit on my own and learned the art of making new friends. People think I’m funny. (I am.) It gets better.