I was taking lisinopril for high blood pressure, but developed a cough. My doctor switched me to valsartan. After a couple of months I developed very dry skin and itchiness all over, but mainly on my scalp. What cam be done?

ACE ARB reaction. Cough is the most common side effect to these class of drugs however your itching is also possibly a drug reaction and another class of hypertension management drug needs to be tried.
As your doctor. likely told you, developing a cough with ACE (angiotensin converting enzyme) inhibitors like lisinopril is quite common. Often switching to the ARBs helps. Dry skin/itchiness is not commonly reported as a side effect of Valsartan so my opinion is it is not related. Aggressively treat the dry skin with sensitive skin moisturizers. If needed, do a trial off Valsartan under your Doctor's supervision.
See a dermatologist. Changing from ACE to ARB got rid of the cough. Your dry- itchy skin is probably not related to valsartan. A dermatologist will help you. Meanwhile take a long bath or shower every night using a skin cleanser such as Dove or Eucerin with a pH of 6 to 7. Immediately after soaking, apply a ceramide cream, rubbing in well. These creams include Eucerin, Aveeno, (oatmeal) CeraVe, generics. Do not heat your home o.
Side effct. Please have the doctor change medicines to a different class of medicine for BP treatment.