I have psoriasis also. I think it is attracted to whatever different ph balance is in the skin with hair. Because I get it on my scalp, eyebrows, around the hairline, behind the ears. I only get it when I stop using a psoriasis shampoo though. As long as I am using one (i have used t-gel, but my favorite one is no longer available) then I get no flair-ups. Or mostly no flair-ups... stress can bring it on, and always a bit at the turn of the season.
The coal tar works too, (best really) but then I came across an article about its carcinogenic effects... so I try to stay away from it as much as possible.
I would think that you have no hair on your head would clear it up altogether. Or is that what you were hoping for by shaving it?
Peace,
tammy