I hate being home for any length of time
Why do you hate staying at home?
Because my mother is too nosy and because I find her very annoying.
I'm sorry your mom isn't the best, so you should just stay out as long as you can. Being at home all the time can drag you down so you need to refresh by going outside sometimes.
What do you mean? I can't just leave the house by myself.
You should try to find some space from your mom. You could enroll in some extracurricular activities after school or get permission to hang out at a friend's house. Eventually you should have a talk with your mom to try to cheer her up.