I've experienced this throughout my life, but I in general am a reserved and quiet person or one could say, independent. I am a senior in high-school now and although I have friends, I prefer to pass my free time (lunch break) alone in the library, and sometimes I'll walk around the school and run errands.
An advice I'd give you is to not care ALOTT for making new friends, while you're in school you WILL make friends in the process so don't worry, don't stress it out.
Remember that you only need the company of yourself (referring to having to find friends) so whenever you are alone in school, simply enjoy the time by doing some homework, watching a movie, playing a game, reading a book, etc... don't let the fact of being alone bother you and make you think that you need someone to be with.
In school, you'll see those with similar interests as yours and you'll most likely attract them with your energy. And for making friends in class, before lunch break you can always talk to someone, and ask them where they go, and therefore you can go with them.
I wish you the best, and I hope you make real friends that are loyal and good. Blessings XOXO