Atopic Dermatitis (Eczema): This is the most common diagnosis for severe full body eczema, especially given the onset since infancy. Atopic dermatitis is characterized by dry, itchy, and inflamed skin, often affecting the face and extremities, and is frequently associated with other atopic conditions such as asthma and allergies.

Seborrheic Dermatitis: Although more common in adults, seborrheic dermatitis can occur in infants and children, causing a red, itchy rash on the face and other areas of the body. It's less likely than atopic dermatitis but should be considered, especially if the rash has a distinctive distribution or appearance.
Contact Dermatitis: This condition occurs when the skin comes into contact with an allergen or irritant, leading to a rash. Given the widespread nature of the eczema, it might be less likely, but it's possible, especially if the child is exposed to a wide range of potential allergens or irritants.
Ichthyosis: A group of skin conditions characterized by dry, scaly, or thickened skin. Some forms of ichthyosis can present with severe eczema-like symptoms and could be considered, especially if the skin has a characteristic appearance or if there's a family history.

Wiskott-Aldrich Syndrome: A rare genetic disorder that affects the immune system and is characterized by eczema, thrombocytopenia, and recurrent infections. It's crucial to consider this diagnosis due to its severe implications and the need for specific management.
Hyper-IgE Syndrome (Job Syndrome): Characterized by recurrent cutaneous and pulmonary infections and extremely high levels of IgE. Eczema is a common feature, and missing this diagnosis could lead to inadequate treatment of the underlying condition and its complications.
Netherton Syndrome: A rare genetic disorder that includes ichthyosis, atopic-like dermatitis, and an increased susceptibility to atopic diseases. It's essential to recognize this condition due to its systemic implications and the need for comprehensive care.

Omenn Syndrome: A rare form of severe combined immunodeficiency (SCID) characterized by eczema, lymphadenopathy, and hepatosplenomegaly, among other symptoms. It's a rare condition but one that would have significant implications for the patient's health and treatment.
Conradi-Hünermann Syndrome: A rare genetic disorder that affects the development of skin, hair, and bones, and can include features of ichthyosis and eczema. It's less likely but should be considered in the differential diagnosis due to its distinct characteristics and the importance of genetic counseling.