Yep, psoriasis can elevate white blood cells. https://www.health.harvard.edu/diseases-and-conditions/psoriasis-more-than-skin-deep From the article: "At a basic level, psoriasis is a disorder of the immune system. White blood cells called T-helper lymphocytes become overactive, producing excess amounts of cytokines, such as tumor necrosis factor, interleukin-2, and interferon-gamma. In turn, these chemicals trigger inflammation in the skin and other organs. In the skin, the inflammation produces three characteristic findings: widened blood vessels, accumulation of white blood cells, and abnormally rapid multiplication of keratinocytes, the main cells in the outer layer of the skin. In healthy skin, keratinocytes take about a month to divide, mature, migrate to the skin surface, and slough off to make way for younger cells. But in psoriasis, the entire process is speeded up to as little as three to five days. The result is thickened, red skin that sheds silvery scales of keratinocytes that have matured before their time"
Have you ever tried any of the over the counter shampoos for your child? My son uses one. The coal tar shampoos are pretty good. They smell a bit like a tire but it's worth it to improve the situation. If the situation is more severe, your doctor can prescribe a treatment. https://www.webmd.com/skin-problems-and-treatments/psoriasis/scalp-psoriasis-treatment Let me know what you think. The article also has a way to remove scales on the scalp to try.