Try the South Beach Diet. Its healthy and can help you lose weight and develop good habits in food choices. I lost 50lbs on it in about 8 months.
What's the south beach diet??
The South Beach Diet is a diet that is low in carbs and bad fats. If you google South Beach Diet it will give you plenty of info. The diet encourages healthy balanced eating and if you stick with it, you can really see some results.
Start using the food tracker on medhelp and see how many calories you are eating each day. Do this for a week without changing your diet. Then after a week, do the calories they suggest for your weight loss goal. At 5'4 you probably can eat around 1800 calories and get weight loss. Walking 30 minutes a day will help and it is low impact for someone with asthma. At your age, you should take your time losing weight as you need to feel good each day to be successful in school.
There is no really fast, way to lose weight healthily. I agree with using the food tracker to see how many calories you are eating each day, then start making small changes, like drinking water instead of soda (including diet soda), or snacking on raw veggies, rather than a candy bar, yogurt in place of ice cream, etc.
Exercise is essential to losing weight AND being healthy. There are exercises you can do that should not bother your asthma. Walking is always good, and you can do it at a pace that shouldn't bother you. Yoga is also good, and it teaches proper breathing, relaxation, etc.
It's safest to lose 1-2 pounds/week; you are still very young and your body is still growing/maturing, so you need to be very careful and make sure you make healthy choices.