If you avoid playing sports because you're deathly afraid of hurting yourself, you might suffer from traumatophobia, or a fear of being physically hurt.
A psychiatrist might diagnose a patient with traumatophobia, also known as "injury phobia," if her fear of getting injured keeps her from living a normal life. Her traumatophobia, for example, could make her too scared to drive a car. The word itself is pretty much the sum of its parts: the Greek word trauma means "wound," and phobia comes from the Greek phobos, or "fear."