It does sound like psoraiasis - get an apt. with your GP.
If he is willing - ask him to prescribe Sinlar Gel and rub it in regularly - daily is ideal. I have next to no hair, so a gloop about the size of a 10p piece does me. I put it on in the mornings - saves staining the pillows. If you have long hair, there is an applicator with it.
I find this very good. For shampoo, use something like Johnson's baby shampoo, or pears, but nothing with any abrasive ingredients.
Hope this helps.