I need to lose 20 pounds in a month HELP !?

Okay so I'm 5'6 218 pounds which is obese & over weight, i have camp in like a month i have to lose weight so my mom will let me go and for my health , DON'T SAY ITS NOT HEALTHY, AND I'M GONNA GAIN IT BACK, because my Dr. said since I'm obese (70 pounds over weight) i can lose it , I started my diet today and i ate half of a fat free low fat yo plait yogurt and 2 hours later a baby carrots and green tea, I'm not hungry now, actually i feel good not stuffing my face. After school I'm gonna workout at the gym for a hour or two jogging on a treadmill, doing sit ups and a few weight lifts, not much, I'm gonna workout 5X a week and walk for a hour on the weekends. & I'm gonna be in swimming, soccer & tennis so I doubt I'll gain the weight back because I'm gonna be eating healthy and very active. do you guys thank i can lose this 20 pounds? Please help me, I'm 14 1/2 and I get talked about every day because Im fat :( I wanna change that and lose weight so in four months when school starts I'll be a whole new person. I'll be able to keep my 4.0 GPA since i won't be stressed out and depressed. Well thanks everyone & have a nice day (: