**Core Concept**
The child's presentation of unilateral nasal obstruction, a cheek mass, and recurrent epistaxis is suggestive of a nasopharyngeal angiofibroma, a rare, benign tumor that primarily affects adolescent males. This condition is characterized by its rich vascular supply and propensity to bleed, leading to recurrent epistaxis.

**Why the Correct Answer is Right**
Nasopharyngeal angiofibromas originate from the sphenopalatine foramen and exhibit a high vascularity due to the presence of numerous blood vessels, including arteriovenous malformations. This vascularity is responsible for the recurrent and profuse epistaxis observed in these patients. The tumor's growth can also lead to nasal obstruction and displacement of adjacent structures, including the cheek mass described in the patient's presentation.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option might be incorrect because it does not accurately describe the typical presentation of nasopharyngeal angiofibroma. While other conditions can cause nasal obstruction and epistaxis, the combination of these symptoms with a cheek mass is more suggestive of a nasopharyngeal angiofibroma.
* **Option B:** This option might be incorrect because it does not account for the tumor's vascularity and propensity for bleeding. While some tumors can cause nasal obstruction and facial deformity, the recurrent epistaxis is a key feature of nasopharyngeal angiofibroma.
* **Option C:** This option might be incorrect because it does not accurately describe the typical location and behavior of nasopharyngeal angiofibroma. While some conditions can cause nasal obstruction and epistaxis, the tumor's origin from the sphenopalatine foramen and its growth into the nasal cavity and adjacent structures are characteristic of nasopharyngeal angiofibroma.

**Clinical Pearl / High-Yield Fact**
Nasopharyngeal angiofibromas are typically found in adolescent males and are often associated with epistaxis, nasal obstruction, and facial deformity due to the tumor's growth into adjacent structures. A high index of suspicion and prompt imaging studies, including CT or MRI, are essential for diagnosis and management.

**Correct Answer:** D.