Hi. Greetings. Yes your child has eczema and this appears to be something called atopic eczema. Both the parents and child require a lot of counseling for this condition. The patient is usually genetically predisposed to this and best treatment and prevention is to keep skin moist by using moisturising and barrier repair creams. Next thing, see a qualified dermatologist and get treated for the problem and take advise for maintenance treatment. Avoid exposure to dust, other allergens like perfumes, cosmetics,etc. Hope this helps. Warm regards. Dr Govind S Mittal.