I tried a lot of things for dry/itchy scalp & years ago the lady who cuts my hair told me to use Paul Mitchell Tea Tree shampoo which works well. Since then, Sally's Beauty Supply came out with a generic that is just as good that I use now. I don't use it everyday, but just once or twice a week if I feel an itch come on. Generally I use Shea Moisture Black Castor Oil shampoo as my go to.
The best thing I've found for dry scalp is just plain organic coconut oil for deep conditioning. Just rub coconut oil into your scalp & cover it with a plastic bag or a throw-away shower cap. Then wrap a towel around that to keep it warm. The oil will melt & coat your hair helping it too. Just wear an old shirt in case the oil drips a little. After an hour or so, just wash your hair as usual.
I use the Aldi organic coconut oil in a jar, it's the same you would cook with. Once in a while I'll find fresh ginger that I'll grate a little & mix it in with the coconut oil. It smells good & makes my scalp feel good. I'll store the whole ginger in the freezer until I need it.
I get dry skin in winter & I found fragrance free products by Gold Bond or Curel Itch-Defense work good. My favorite is Marcha Labs Wood Wax Cream which is very thick & contains lanolin in it. I find a little goes a long ways & I don't have to use it everyday. You can order it directly from Marcha Labs or on Amazon.