Just speculating here, but I know that many conditions like fibromyalgia are aggravated by sleep deprivation. Sleep deprivation also makes you more irritable, so a minor dry skin itch becomes noticeable and bothersome. read more
The vasodilation in your cutaneous tissue causes an itchy feeling (similar to the itchy feeling you get when you fatigue a muscle in an intense calisthenics workout). My 2nd theory - it’s paresthetic: Sleep deprivation increases stress, which can increase our awareness of sensations (particularly pain). read more
Take this 2009 study in Sleep: researchers asked both sleep-deprived and well-rested volunteers to perform a set of tasks that required quick decision-making two times. Between testing, the accuracy of those without quality sleep went down by 2.4%, while the rested group improved accuracy by 4.3%. read more