Egads, it sounds to me like you have an allergy, especially if your scalp is stinging.  I'd get myself to a doctor right away and see what the problem is.  Your situation is very unusual, there's no reason this should happen no matter how often you wash your hair.

Once you rule out or resolve any allergy issues, I suggest you try natural hair care products such as Nature's Gate.  And make sure that you don't scratch your scalp or use very hot water when you shampoo.  Be gentle!