**Core Concept**
The underlying clinical principle being tested is the diagnosis of a specific condition affecting the coccyx in a pediatric patient, based on clinical and radiographic findings.

**Why the Correct Answer is Right**
The clinical presentation suggests a case of _Coccygeal Hematoma_, which is a collection of blood in the soft tissues surrounding the coccyx. The absence of a cough impulse helps to rule out a _Coccygeal Abscess_, which would be more likely to produce a palpable impulse on coughing. The X-ray finding of erosion of the coccyx is consistent with a hematoma, which can cause erosion of the underlying bone due to increased pressure and blood accumulation.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is not relevant to the clinical scenario, as it does not describe a condition affecting the coccyx.
**Option B:** A _Coccygeal Abscess_ is unlikely in this case, as there is no mention of fever, redness, or pus, which are typical features of an abscess.
**Option C:** A _Coccygeal Fracture_ may occur in adults, but it is less common in infants and would not typically present with a swelling in the sacral region.

**Clinical Pearl / High-Yield Fact**
Coccygeal hematomas are a common cause of swelling in the sacral region in infants, often resulting from trauma during delivery or a minor fall.

**Correct Answer:** C.