**Core Concept**
The question is testing the ability to diagnose a nasal swelling in a child, which involves understanding the anatomy and common causes of nasal masses in this age group. The root of the nose is a specific area where certain types of swellings are more likely to occur.

**Why the Correct Answer is Right**
The compressible swelling at the root of the nose in a 2-year-old child is most likely a **nasal glioma**. A nasal glioma is a rare, benign tumor-like lesion that arises from the remnants of the embryonic neural tissue at the root of the nose. It is composed of glial cells and is usually present at birth or appears in early childhood. Nasal gliomas are typically compressible and non-pulsatile, and they can cause nasal obstruction and other respiratory symptoms.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option is not provided, so we'll skip it.
* **Option B:** A nasal polyp is a common cause of nasal obstruction, but it is usually not compressible and is more likely to present in older children or adults.
* **Option C:** A nasolabial cyst is a type of skin cyst that can occur along the nasolabial fold, but it is not typically located at the root of the nose and is not compressible.

**Clinical Pearl / High-Yield Fact**
Remember that nasal gliomas are usually benign and do not require surgical excision unless they cause significant symptoms or are suspected to be malignant.

**Correct Answer: C. Nasal glioma.**