Try to buy a swiss ball. They're pretty small so you can maybe even fit it in your room where no one can watch you and only $20 and they usually come with a workout dvd. What's cool about the ball is that it always works your 'core' region because you have to keep balance. I'm not some professional, I've just noticed this with my swiss ball.
Do you have healthy foods at school? My school has a minimum 5 lunch choices and a salad bar, I eat a ton of vegetables there and there's always at least a healthy food there.
Do you have a bike? Maybe you can try riding a few miles a day.
Just kind of concerened because when I was 15 I was kind of out of shape, then at 16 I got into really great shape, weight and muscle wise. Now I'm 18 and just feel flimsy, I'm trying gain some muscle back.
As far as eating healthy, I just reccomend trying to eat 1 serving of food and then stop. By 1 serving I don't mean just 1 meal such as an apple, I mean something like, 1 drink, 1 meal, 1 vegetable/ fruit that's prettygood. At 15, your metabolism might be fast (mine was) and I could get away with eating extra/ unhealthy food so even if I didn't stay strict I still lost weight.
I started dieting at 15 so I can tell you exactly what I did. Eat eggs for breakfast w/ milk and or toast. Lunch I kept small, a sandwich type meal, milk, and raw vegetables. For dinner I would eat a family cooked meal, rice, pasta, etc, and I would eat one or two helpings at the time.
At first I just did situps and pushups, I was getting fit so fast fast a dude at school even accused me of using steroids. I was the same height as you, about 5'10-5'11 (I'm still 5'11) and I weighed about the same, between 166-175.
Some professionals can probably tell you better, just trying to say what I did.