**Core Concept**
The child's presentation of itchy, exudative lesions on the face, palms, and soles, along with similar complaints in the siblings, suggests a diagnosis of scabies. Scabies is a skin infestation caused by the mite Sarcoptes scabiei, leading to a severe allergic reaction and intense itching.

**Why the Correct Answer is Right**
The management of choice for scabies involves the use of topical or oral antiparasitic agents to kill the scabies mites and their eggs. Permethrin cream is a topical treatment that is commonly used for scabies, while ivermectin is an oral medication that is effective in treating scabies, especially in cases where topical treatments are not feasible. Both permethrin and ivermectin work by killing the scabies mites and preventing them from laying eggs, thereby breaking the scabies life cycle.

**Why Each Wrong Option is Incorrect**
**Option A:** Oral antihistamines alone are not sufficient to manage scabies, as they only alleviate the symptoms of itching and do not kill the scabies mites.

**Option B:** Topical corticosteroids may provide temporary relief from itching but do not address the underlying scabies infestation.

**Option C:** Using only soap and water to clean the affected areas is not an effective treatment for scabies, as it does not kill the scabies mites or their eggs.

**Clinical Pearl / High-Yield Fact**
In cases of scabies, it is essential to treat all household members and close contacts simultaneously to prevent re-infestation.

**Correct Answer: C. Topical permethrin cream or oral ivermectin.**