There are a few options for a dry, itchy scalp. At-home remedies or ingredients to look for in products would be tea tree oil, coconut oil, peppermint oil, and zinc, as they tend to be soothing to the scalp and won't dry it out. It will also help to wash your hair every 2-3 days if possible and avoid harsh fragrances as they can irritate your skin.
As far as a purchasable product, I recommend the Nioxin Scalp Recovery Soothing Serum
. They also carry a Shampoo and Conditioner if you like the line and would like to try all of their products. I hope this helps!