I have the same problem and it's called psoriasis, but looks like the scalp is more infected than me
My Psoriasis is less aggressive since i stopped eating refined sugar
I'm lucky i get rashes in the scalp, eyebrows and mustache area only.
On the mustache area i shave few times per week with old school shaving products (
@rand anon) so it rarely happens.
For eyebrows i have hydrocortisone and cortisone creams i can apply on the eyebrows before going to bed and then wash the face with a salicylic acid based face wash with urea etc
For scalp same thing, few days of cortisone and then washing it with selenium sulfide, zinc pyrithione or piroctone olamine based shampoo