This is eczema
. It is a very classic presentation of eczema, especially the permanence of the rash and the areas of the body where you have it. Eczema is a chronic condition caused by a lack of certain moisturizing elements in the skin, which leaves the skin red, dry, and itchy. Sometimes, it takes a few tries to get the right prescriptions in place for the eczema, as each person is different. Therefore, you need to go back to your dermatologist
and explain what you experienced with the last round of medicines so that they can help you adjust your regimen.
Also, as you have noticed, the rash responds to using soft soaps and moisturizing. This is the mainstay of what you can do at home for the eczema. You should avoid prolonged or frequent showers, especially with hot water, as this just dries out the skin. At least once a day, but preferably multiple times a day, you should apply a good moisturizer. The best moisturizers are the thick, greasy ones like hydrolated petrolatum. Other standard lotions and creams are too thin to be of much value.
Daily moisturizing is supplemented by applying steroid creams as prescribed by your dermatologist.