Eczema can have different root causes. The rash is merely the skin's reaction to whatever is going on, whether it is topical or internal. I would encourage you to find and target the root causes rather than treating the reaction. Suppressing the skin's reaction can cause the reaction to break out deeper within the body.
I had eczema for many years, and for me, it turned out to be my tap water that was causing it. A shower filter from WaterWise, and a pair of rubber gloves at the kitchen sink cleared up my skin.
Eczema can also be caused by food intolerances, unhealthy gut flora, toxins, etc.
I'm sure there are already threads on here about eczema.