Acne Vulgaris: This condition is common in pre-teens and teenagers, characterized by comedones, papules, pustules, and sometimes cysts on the face. The improvement with antibiotics supports this diagnosis, as antibiotics are often used to treat moderate to severe acne.

Impetigo: A highly contagious bacterial skin infection that can cause pustules on an erythematous base. It improves with antibiotic treatment, which aligns with the provided history.
Folliculitis: An inflammation of the hair follicles, which can be caused by bacterial infection and presents with pustules. It can improve with antibiotic therapy.
Keratosis Pilaris with Superimposed Infection: While keratosis pilaris itself does not typically present with pustules, if there is a superimposed bacterial infection, it could lead to pustule formation and improve with antibiotics.

Staphylococcal Scalded Skin Syndrome (SSSS): Although less common in older children, SSSS is a serious condition caused by staphylococcal toxins that can lead to widespread skin exfoliation and requires prompt diagnosis and treatment.
Infectious Eczematoid Dermatitis: A condition that can mimic eczema but is caused by an infectious agent. It's crucial to differentiate it from other dermatitis forms due to its need for specific antimicrobial treatment.

Pustular Psoriasis: A rare form of psoriasis characterized by the widespread appearance of pustules. It's less common in children but can occur and may have a varied response to treatments, including antibiotics in cases of superinfection.
Autoinflammatory Disorders (e.g., PAPA Syndrome): These are rare genetic disorders that can cause recurrent episodes of skin pustules among other systemic symptoms. They are important to consider in cases where common diagnoses do not fit or when there's a significant family history of similar conditions.