How can I lose weight/stay fit?

I weigh a little over 110 pounds and I'm 5'3. Its unhealthy, but I want to lose 15 pounds (so I'm 95 pounds) before school starts. Problem is, my parents don't let me go anywhere without them, unless I'm with friends, and they won't go running with me or bike riding either, so I need to lose weight from jumping jacks, and running laps in my bedroom. And as for dieting, I need a way to stay away from cookies and fattening stuff, so tricks to do that. And last thing, I'm NOT going anorexic. Please help?