The correct answer is B. Mineral oil prep.
This clinical image and scenario most likely represents Infantile acropustulosis (IA), which is a benign vesiculopustular condition with an often chronic course in infants. The etiology is unknown. Some studies suggest that African-American male infants are more commonly affected. IA is characterized by recurrent crops of intensely pruritic vesiculopustules on the palms and soles. The diagnosis is based on clinical features and given the similar appearance, scabies should be ruled-out with a mineral oil prep.
The other tests are generally not necessary in this clinical scenario. If a skin biopsy is performed, it would demonstrate a subcorneal pustule with neutrophils and eosinophils.
References: Mancini AJ, et al. Infantile acropustulosis revisited: history of scabies and response to topical corticosteroids. Pediatr Dermatol. 1998 Sep-Oct;15(5):337-41. [https://www.ncbi.nlm.nih.gov/pubmed/9796580]