**Core Concept**
The patient's presentation is suggestive of a hernia, specifically an inguinal hernia, given its location below and lateral to the pubic tubercle. Inguinal hernias can become incarcerated or strangulated, leading to bowel obstruction and potential necrosis.

**Why the Correct Answer is Right**
The correct answer involves surgical intervention to relieve the obstruction and prevent further complications. Given the patient's age and the presence of intestinal obstruction, prompt surgical repair is necessary to avoid bowel ischemia and necrosis. The goal is to reduce the hernia and restore blood flow to the affected bowel segment.

**Why Each Wrong Option is Incorrect**
**Option A:** Administering antibiotics without addressing the underlying cause of the obstruction is inadequate and may lead to further complications.
**Option B:** Continuation of conservative management with nasogastric tube and intravenous fluids is insufficient for a strangulated hernia, which requires immediate surgical intervention.
**Option C:** The use of a mesh plug or other non-surgical repair methods may not be suitable for a strangulated hernia, which requires a more definitive surgical approach.

**Clinical Pearl / High-Yield Fact**
In cases of suspected hernia strangulation, prompt surgical intervention is crucial to prevent bowel necrosis and improve outcomes. A delay in treatment can lead to significant morbidity and mortality.

**Correct Answer:** C. Prompt surgical exploration and repair of the hernia is the next step in treatment to relieve the obstruction and prevent further complications.