i have absolutely horrible scalp psoriasis.. it is BAD..
no shampoos help it.. only a solution that is available by prescription called fluocinoline acetonide 0.01%.. it is also available in a brand name called derma-smooth scalp oil but that is like $100+ dollars.. so i had the doc write for the generic chemical name to save lots of money (the generic doesn't convert if brand name is written so you must have it written specifically for the generic to get the generic).
anyways, i swear by this stuff. i love it. i just got it again after years of going without, and boy does my scalp thank me.
good luck whatever you do!