Dyshidrotic Eczema: This condition is characterized by intense itching and erythema on the palms, often accompanied by vesicles. It's a common cause of palmar pruritis and erythema, making it the most likely diagnosis.

Contact Dermatitis: This is an allergic or irritant reaction to substances that come into contact with the skin, leading to pruritis and erythema. Given the exposure of palms to various substances, contact dermatitis is a plausible cause.
Atopic Dermatitis: Although more commonly associated with flexural areas, atopic dermatitis can involve the palms, especially in individuals with a history of atopy.
Psoriasis: Palmar psoriasis can present with erythema and pruritis, and while less common than other forms of psoriasis, it remains a consideration in the differential diagnosis.

Scabies: Caused by the mite Sarcoptes scabiei, scabies can lead to intense pruritis and erythema, particularly in interdigital areas. Missing this diagnosis could lead to prolonged suffering and transmission to others.
Pompholyx: A form of hand eczema that can present with vesicles and intense itching, pompholyx is important not to miss due to its potential to significantly impact quality of life.

Keratoderma Blennorrhagicum: Associated with Reiter's syndrome, this condition presents with erythematous, keratotic lesions on the palms and soles, and is a rare but important consideration.
Pityriasis Rubra Pilaris: A rare skin disorder characterized by constant itching, palmoplantar keratoderma, and erythematous orange patches, making it a rare but potential cause of palmar pruritis and erythema.