jrdivagrl,
Thyroid issues are very, very frustrating. I have worked with several women over the years with this type of condition, and it truly does seem that no matter what you do right, the weight does not want to come off. That said, exercise can help things stabilize, and following your doctor's advice, even when away from home, will be imperative to your long term success.
At 14yo, injuries you sustain will have a greater impact on the rest of your life than when your body stops growing. It is critical that you get proper instruction to ensure you are completing exercises with the right technique, to the right intensity, and with the right frequency.
I post workouts weekly (though I was slack this week because of a sick dog) at
http://www.divefitness.com/html/workouts.html . You can get an idea of what I feel an adult diver should be doing weekly to stay in shape for diving. Coincidently, the "Zero to Hero" plan is the same type of schedule that might help you.
If you were my daughter and instruction were available, I'd get you involved with some type of formal fitness instruction, whether it's a group class or individual training. It will help you get started on the right track.
If that is not available to you, I list three books on the webpage above that can help you to learn the proper form for many useful exercises.
Cameron