Losing weight for teens with asthma?

so I am 16 and overweight, I'm 5'6'' and 220 lbs 32.4% body fat and have been looking into many diets and exercises, most thing say eat smaller portions, or eat more fruit, but the thing is that I hardly eat, for example I haven't eaten since lunch yesterday and I am still not hungry, and when I do get hungry I usually eat an apple or a some chicken maybe a small salad and then I go without eating again for about another 3-5 hours. I would like to get more into the extensive cardio, but I have horrible asthma and suffer from EIB which is usually easy to control, but not mine for some dumb reason. I was thinking of getting in to kickboxing, and was going to try out for the high school soccer team if I can get my endurance and stamina up, and of course get my asthma under control. I can only do short bursts, I can't keep up for over 30 seconds before my asthma starts getting unbearable. Losing weight is important to me because hypertension and diabetes run in my family. I guess all I am asking for is dieting techniques that might work with how little I eat, and an exercise that will build up my tolerance to asthma attacks so I don't collapse in the middle of an exercise.