I'm afraid to say it, but that's just the nature of the game at 16. It only really changes, in my experience at around 18+, especially if you go to university.
Personally, I'd suggest you grow some thick skin, don't let it bother you and gain the attitude - it's not what you can do for them, it's what they can do for you. But you need to be confident enough to actually realise this.
Moving school sounds like a good idea as you can aim to meet new people, but bare in mind; it doesn't always work out. I left school, went to college - met no one, dropped out and went back to sixth form. I have met so many new people who consider me a friend, etc since I was 16 it's quite strange. By very definition, I'd describe myself as popular, yet I still feel the same as I did when I was in your position, albeit the paranoia no longer exists. I don't 'feel' popular but I know I have lots of friends and a very active social life.
It's hard to describe, but if you're a good enough person - people will eventually rather be around you then push you away.