I have had scalp psoriasis for over thirty years and still can't get rid of it. I have been to several dermatologists and used prescriptioned shampoos that were specially mixed, every type of shampoo that you can buy over the counter and still can't get rid of it. Right now I'm using Redken All Soft shampoo because my hair started to feel like straw using the medicated shampoos. It has helped but when I get stressed the itching becomes terrible and I constantly scratch my scalp.
I fully understand what you are going through. I don't know if this shampoo will help you, but it has helped me tolerate the itching.