**Core Concept**
The child's presentation of an expansile swelling on the medial side of the nose suggests a potential mass lesion involving the nasal cavity. This could be due to a variety of causes, including benign or malignant neoplasms, inflammatory processes, or congenital anomalies.

**Why the Correct Answer is Right**
The correct answer is likely a **Nasolabial Dermoid Cyst**. A nasolabial dermoid cyst is a congenital anomaly that arises from the fusion of the nasal and labial prominences during embryonic development. It typically presents as an expansile swelling on the medial side of the nose, often associated with a midline nasal mass. The cyst contains a mixture of skin, bone, and soft tissue elements, which can lead to its characteristic expansile growth.

**Why Each Wrong Option is Incorrect**
**Option A:** A **Nasal Polyp** is a common condition characterized by an inflammatory mass within the nasal cavity, but it typically presents with nasal obstruction, congestion, and rhinorrhea, rather than an expansile swelling.
**Option B:** A **Rhabdomyosarcoma** is a malignant tumor of the soft tissues, which can occur in the head and neck region, including the nasal cavity. However, it typically presents with more aggressive symptoms, such as pain, bleeding, and rapid growth.
**Option C:** A **Nasal Adenocarcinoma** is a malignant tumor of the nasal cavity, which can present with a mass lesion, but it is typically associated with more advanced symptoms, such as nasal obstruction, epistaxis, and facial pain.

**Clinical Pearl / High-Yield Fact**
Nasolabial dermoid cysts are typically diagnosed in the first two decades of life and are more common in males. They can be associated with other congenital anomalies, such as cleft lip or palate.

**Correct Answer:** D.