"I'm not ashamed of my green hair."
Translation:Je n'ai pas honte de mes cheveux verts.
Because in French you neither "brush your hair" nor "brush the hair." Instead, you "brush for yourself the hair" (Je me brosse les cheveux)
So I can be ashamed of MY hair. Not "ashamed for myself the hair."
Because "Je n'ai pas honte de.." does not have the reflexive "me" in it. So you must add "mes cheveux." in order to show that you're not ashamed of your own hair.