An itchy, burning scalp can be caused by your shampoo. With extremely dry skin, or skin that is susceptible to atopic dermatitis, it is often very much a matter of choosing the right shampoo.
Those who believe they can alleviate extremely dry skin and dandruff with an anti-dandruff shampoo are frequently wrong. On the contrary, anti-dandruff shampoo is harsh for the skin which may cause more itching and burning sensation.
A suitable shampoo will not dry out the scalp and should gently cleanse the hair and scalp.