This patient has cutaneous larva migrans, and the most appropriate treatment is oral ivermectin. Cutaneous larva migrans (creeping eruption) is a parasitic skin disease caused by migration of the hookworm larvae within the superficial layers of the skin. It presents as a pruritic serpiginous, linear, or arciform red plaque that migrates at a rate of a few millimeters to centimeters per day and represents a hypersensitivity reaction to the hookworm, most commonly Ancylostoma braziliense. The clinical appearance of a migratory pruritic plaque after exposure to a beach is characteristic of cutaneous larva migrans. Although cutaneous larva migrans can be self-limited, treatment with oral ivermectin (or albendazole) is the medication of choice.
Oral cephalexin is an antibiotic that is used for bacterial skin infections, which may occur secondarily in patients with cutaneous larva migrans at times, but the lack of honey- or yellow-colored crust and surrounding erythema in this patient make a bacterial infection unlikely.
Oral prednisone may be helpful for the symptoms associated with cutaneous larva migrans, but it is not necessary or first-line treatment (topical glucocorticoids can be used for severe pruritus); oral prednisone would be the treatment of choice for allergic contact dermatitis, which can be geometric (rectangular, circular, even serpiginous) in shape, but should not migrate.
Terbinafine is the treatment of choice for dermatophyte infections, such as tinea pedis, which presents on the feet and ankles. Dermatophyte infections can be annular in appearance but differ from the clinical picture here in that it usually has superficial scale in a “moccasin” distribution or annular configuration, maceration between the web spaces and does not migrate. It would not be effective against this parasitic infection.