Impetigo: A common, highly contagious skin infection in children, often presenting with ulcerating papules, especially if the rash is unilateral. It's caused by Staphylococcus aureus or Streptococcus pyogenes.

Eczema (Atopic Dermatitis): Can sometimes present with ulcerations, especially if scratched, and may appear unilateral, though it's typically bilateral. It's a chronic condition characterized by dry, itchy skin.
Insect Bites: Could cause a unilateral rash if the child was exposed to bites on one side of the body. The bites can become ulcerated if scratched.
Contact Dermatitis: An allergic reaction or irritation from something that came into contact with the skin, which could present unilaterally and cause ulcerating papules.

Child Abuse: It's crucial to consider non-accidental injury, especially if the rash or ulcers have a pattern suggestive of inflicted trauma.
Staphylococcal Scalded Skin Syndrome (SSSS): Although more common in infants, SSSS can occur in toddlers and presents with widespread skin lesions that can start unilaterally, progressing to a more generalized rash.
Herpes Simplex Virus (HSV) Infection: Can cause localized, painful ulcers, and while less common in this presentation, it's a critical diagnosis not to miss due to potential for serious complications.

Bullous Pemphigoid: An autoimmune blistering disease that can rarely occur in children, presenting with large blisters that may ulcerate.
Epidermolysis Bullosa: A group of genetic conditions that result in fragile skin and blisters, which can ulcerate, often from minor trauma.
Cutaneous Leishmaniasis: Depending on the geographical location, this parasitic infection can cause skin ulcers, though it's uncommon in many areas and typically associated with travel history or endemic regions.