Dear Here we go:
Thanks for the additional information.
Why do you assume that being injury-prone has to do with your weight? I can think of no less than twenty "big" causes of injury. Injuries can be the result of multiple factors, namely;
1. Doing too much, too soon
2. Bad technique
3. Being tired
4. Doing something you are physically not ready for
At your age, being injury-prone raises some SERIOUS red flags. Your body is still developing and "dieting/losing weight" is NOT the answer.
You still did not mention what your is ultimate training goal. What event(s) you hope to compete in.
I can tell you that you are almost definitely not hitting either your micro nor macro-nutrient requirements (vitamins, minerals, calories). This in turn, will affect your hormonal profile. This is a very, very, very serious matter given your gender AND age. You are potentially compromising your fertility (you may one day want to become a mother) and setting yourself up for osteoporosis (weak bones, constant injuries, height loss, poor athletic performance).
PLEASE, PLEASE, PLEASE speak with your parents FIRST, then your primary-care physician, then a sports-performance nutritionist, then your sport-coach, and finally your personal trainer.
Take care of yourself !!!