If the rash is bright red, raised, warm, or spreading and if there is fever
then this could be a sign of a skin infection and you would need to seek immediate medical care. However, this does not sound like what is going on.
It sounds more likely that you have developed dry skin or a contact dermatitis. Contact dermatitis is an inflammation of the skin that is caused by exposure to some chemical or allergen, usually something like a new soap or personal care product or laundry detergent. Treatment involves stopping the offending agent as well as using a topical steroid cream to get the itching under control.
Dry skin, or eczema
(which is the more severe, chronic form of dry skin), causes inflammation, itching, and redness of the skin. It is common in winter months. Avoiding hot water and soap is important to prevent further irritation. Daily skin moisturizing with a thick, greasy moisturizer like hydrolated petrolatum is also important and, also, many cases require a steroid cream to get under control.
I suggest first talking to your primary care doctor
, as they will be able to look at the rash and help you decide what is going on and what treatment is appropriate.