Differential Diagnosis for Rash on Both Arms in a 5-Month-Old Infant

Single Most Likely Diagnosis

• Tinea corporis (Ringworm): This is the most likely diagnosis given the initial ring-shaped formation of the rash, lack of response to antifungal treatments (though this could be due to inappropriate use or resistance), and recurrence after a holiday, potentially exposing the child to new fungal strains. The rash's characteristics and the child's age support this diagnosis.

Other Likely Diagnoses

• Eczema (Atopic Dermatitis): Although the family history is negative for eczema and the child has not had similar issues before, eczema can present at any age and may not always follow a clear familial pattern. The description of the rash as erythematous and macular with rough skin could be consistent with eczema, especially if the child has been exposed to new environmental factors during the holiday.
• Contact Dermatitis: This could be a possibility if the child came into contact with an allergen or irritant during the holiday, leading to a skin reaction. The lack of itch might make this less likely, but it's still a consideration.
• Impetigo: A common skin infection in children, impetigo can cause erythematous macular rashes. However, it typically presents with more purulent lesions and might not fully explain the ring-shaped initial presentation.

Do Not Miss Diagnoses

• Congenital Syphilis: Although rare, congenital syphilis can cause a variety of skin rashes, including maculopapular rashes. Given the potential severity of missing this diagnosis, it's crucial to consider it, especially if other explanations are not forthcoming.
• Meningococcemia: This is a life-threatening condition that can cause a rash. Although the child is otherwise well and there's no mention of fever or other systemic symptoms, any rash in a child warrants consideration of serious conditions like meningococcemia.

Rare Diagnoses

• Pityriasis Rosea: This condition can cause a rash but typically starts with a herald patch followed by a wider rash, which might not fit perfectly with the described ring-shaped initial presentation.
• Keratosis Pilaris: A condition that causes rough patches on the skin, it might not fully explain the erythematous macular rash described but could contribute to the rough skin texture noted in the objective findings.