Dries skin out. Solvents like water (especially hot water) & soap dry the skin out & make eczema worse. Soap dissolves oil in water, washing away the natural waterproofing barrier that keeps you from drying out. Hot water worsens this by wicking away some of your own moisture as it evaporates off your skin. Applying cream immediately after showering helps prevent some of this moisture loss.
See a dermatologist. Showers or baths, hot or cold, do not aggravate eczema. Caustic soaps such as ivory will make you worse. Dove, eucerin, and others have the correct ph for your skin. Be sure you apply a cream with ceremides immediatly after washing. Eucerin, cereve, neutrogena and others are easy to find. You need a prescription if you are itchy. Antihistamines do not help eczema.