I'm really sorry, this sounds horrible! In the past I've had problems with shampoos and conditioners and I've recently switched to ones without sulfates, dyes, parabens, these sort of things and it's really made a world of difference! Good luck and I hope this helps a bit! :)
Hi, welcome to the forum, this seems to be a form of allergy known as contact dermatitis. The allergen can be in the form of hot water bathing (temperature factor), low humidity environments, xerosis (dry skin), overheating of skin, and exposure to soaps, detergents and others.
Avoiding these situations is helpful for acute flares as well as for long-term management.
In such condition maintenance of adequate hydration of the skin is quite important. Which includes thick creams (eg, Eucerin, Cetaphil, Nutraderm), which have a low water content, or ointments (eg, petroleum jelly, Aquaphor, Petrolatum), which have zero water content, are better.
Along with above measure use of anti histamines and corticosteroids will help to reduce itching (if present) of the skin as well as rash.
I suggest you to consult dermatologist. Take care and regards.