Try changing your body image, not your weight. You are already below the weight you should be at your height and especially at your age. You don't need to be worrying about that at all right now. Are you going to be starting high school this year? Just focus on how fun and new it will be, NO ONE will be looking at you and thinking how many pounds you need to lose. Everything you are considering doing is either way to much exercise for you or is too little calories. When I want to feel healthy, I just don't eat extra stuff that's bad for you like ice cream and candy. If you already do that then you have nothing to worry about.
What is the whole obsession with being "skinny"? For the love of Pete, it's not important. You need to do something with your ego--because it's not your weight that's the problem.