an emollient cream/moisturiser several times a day, and replacement of soap with a non-soap substitute (go to your pharmacy) is the way to go. i would not use a hydrocortisone cream in this instance.
in case that was too confusing, go to your pharmacy, get the pharmacist to look at it, and supply an appropriate moisturiser (preferably non greasy, non irritant) as well as soap substitute
have fun, sounds shitty. hopefully its just dry skin, but cannot exclude something like eczema without doing an assessment
cu