Is it possible that a 240lb 16yr old female lose 100 lbs in 9 months?

Yes. To lose 100 lbs over 9 months, you would have to take in 1300 calories less per day (or burn 1300 calories more per day) than currently. The combination of diet and exercise is always the best.
Possible. Such dramatic weight loss is possible. It would hopefully occur under a doctor's care. Such weight loss occurs with bariatric surgery, but a sustained restrictive diet can do this.
Yes, Might take year. You must aggressively change your lifestyle. Mobile Health games can help. Physicians recommend water, increased veggie intake and walking 10k steps a day. Changing your behavior is HARD! Here is a health game that will help! Commit to tracking your nutrition and weighing in weekly. Losing just 10 pounds can reverse diabetic state.