Vaseline helped my youngest son when he was a child, which was what I was going to suggest. Eczema as well as other skin conditions have been linked to dysbiosis, an imbalance in the intestinal flora. The skin is an outward manifestation of what is going on inside the body. My recommendations are, like the others have stated, include diet, eliminate as much sugar, and processed food as possible. Sugar feeds fungus, and yeast thereby contributing to the problem. Include fresh fruits, and vegetables, these will supply pre-biotics that feed the good bacteria in the intestines. Probiotics to supply, and replenish the good guys, that fight off infection. Include plain yogurt in the diet, as well. If the ezcema is in fact a fungus infection, it will respond to topical applications of plain yogurt. Another topical and natural anti infective is olive leaf, it is gentle enough to not Flare the condition, or make it "angry" apply before bedtime, and leave on. Remove in the am with, a gentle splash of water. Do not scrub.
I am going to assume that youve already gone the route of discontinuing all makeup, and creams, in an attempt to see if its just an allergic reaction. A food diary may also be helpful, as food allergies may also be the culprit.
Resent clinical trials have found a link between vitamin D3, and chronic skin conditions. If you live in the north, chances are you're deficient. 20IU per pound of body weight is the usual therapeutic dosage for chronic conditions.
As well as topical applications to affected areas. A cream has recently come on the market for skin conditions. A liquid gel cap punctured with a straight pin, squeeze the capsule, and apply topically to the affected area.
I have written an article about skin conditions https://hubpages.com/health/Natural-Supplements-fo...
which contains doseage amounts, and were to obtain the suggested supplements.
I hope this helps