I am in a constant battle with myself.?

Go see a doctor. The hair loss is most likely caused by the stress of having this disorder. You either need some sort of therapy or pill, to stop/dull down the thoughts that eating is bad. Eating is good. Even if you don't feel like you need to eat, you should eat. Since you're so skinny, you really need to eat constantly until you weigh more. Look up what the normal Body Weight Index or the normal weight of someone your height is.