**Core Concept**
A two-month-old baby presenting with epiphora (excessive tearing) and regurgitation suggests an issue with the nasolacrimal duct or the esophagus. The nasolacrimal duct is a tube that drains tears from the eye into the nasal cavity, while the esophagus is the tube that carries food from the mouth to the stomach.

**Why the Correct Answer is Right**
The most likely diagnosis in this case is a nasolacrimal duct obstruction. This occurs when the nasolacrimal duct, which is a small tube that connects the eye to the nasal cavity, becomes blocked. This blockage prevents tears from draining properly, leading to epiphora. In addition, the increased pressure in the nasolacrimal duct can cause regurgitation of milk during feeding. The nasolacrimal duct obstruction is often associated with a condition called congenital dacryocystitis, which is an inflammation of the nasolacrimal sac.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option is incorrect because it does not relate to the symptoms described. A cleft palate is a congenital defect that affects the roof of the mouth, but it does not typically cause epiphora or regurgitation.
* **Option B:** This option is incorrect because it is not a common cause of epiphora and regurgitation in a two-month-old baby. A tracheoesophageal fistula is a congenital defect that involves an abnormal connection between the trachea and the esophagus, but it typically presents with symptoms such as choking or coughing during feeding.
* **Option C:** This option is incorrect because it is not a direct cause of epiphora. A patent ductus arteriosus is a congenital heart defect that involves the failure of a blood vessel to close after birth, but it does not typically cause symptoms related to the eyes or the esophagus.

**Clinical Pearl / High-Yield Fact**
In infants, a nasolacrimal duct obstruction can often be diagnosed by applying gentle pressure to the lacrimal sac, which can cause the blocked duct to open and allow tears to drain properly.

**Correct Answer:** C.