I've found that if I use soap on my face I get breakouts, and shampooing my hair always makes it worse. Pits, feet, and balls absolutely need soap, though.
I had trouble with sheets that were freshly washed, they felt irritating to sleep on. it would go away after a day and the sheets would feel soft.
I switched to SLS-free laundry detergent and everything was awesome.
I also did the same with shampoo and my scalp seemed to be better. toothpaste too.
You might want to see if that makes any difference.
Edit: the latter is available online, but it contains Sodium Coco-Sulfate made from plants.
I also used ecos, that disappeared from costco. There was a detergent from all (all fresh clean essentials sulfate-free), but that became hard to get. I now use a detergent called puracy.
This happens on all your skin but it's more egregious on the face because the skin is more delicate there.
No idea for the shampoo though.
Do you use a conditioner after shampoo and how frequently do you shampoo?
Many shampoos can be too abrasive or contain chemicals which can be irritating for you. You might want to switch to baby version of skin products which irritate you. Sometimes, those will irritate less or not at all.
Use liquid soap which can be mixed with water instead of one that has to be applied directly to your skin.
There are bunch of tests to figure out these products for you at dermatologist.