I would encourage looking from an ayurvedic standpoint to treat eczema. Know your dosha type. Dry itchy type eczema is typically Vata imbalance (burning eczema is Pitta, oozing eczema is Kapha). Avoid allergens as it is likely an autoimmune disfunction triggered by offending agents. Vata dosha is inherently dry and light so it makes sense eating heavy moist cooked foods. Cooking helps eliminate many of the naturally occurring enzyme inhibitors and immune triggering compounds, so avoid overeating raw foods. This can make a huge difference.
Watch out for proper ratio of omega 6 to 3. The right ratio is 4:1 so don't exceed on the 3s if you are limiting the 6s. If your vata dosha you need good levels of saturated fats (coconut oil, ghee).
Homeopathics can be very good in conjuction with diet that is right for you; constant worrying about the condition suffocates inherent knowledge of selfhealing so it is wise to put mind at ease by following a more innate subconscious approach (listening to the body) rather than an enforced external protocol promoted by an overwhelmed conscious. Meditation is good to align oneself.