I recently (2 weeks) shaved my head due to treatment and a couple of co-workers who went through breast cancer suggested I start using "up&up hydrocortisone cream 1%" - I put it on every night after I shower and clean my head with mild shampoo and conditioner (I know that sounds weird since I have so little hair, but I want to keep it clean and soften up the little remaining hairs - so far although a sensitive my head is doing okay).

I also keep my head uncovered as much as possible as I find hats irritate the skin a lot more than just leaving it to the air...

Sleeping is when I notice the irritation most - So I sleep in a was soft beanie I got on Amazon: https://www.amazon.com/dp/B019ONNQNQ/ref=cm_sw_r_cp_apa_glt_fabc_ZP1QF216CT6NC6BWH6K5?_encoding=UTF8&psc=1

I hope these suggestions help.