**Core Concept**
The first investigation for a lactating woman presenting with breast pain should focus on differentiating between physiologic and pathologic causes. This involves assessing the severity and characteristics of the pain, as well as evaluating the possibility of underlying conditions such as mastitis or abscess formation.

**Why the Correct Answer is Right**
The correct answer is **Galactography**. Galactography, also known as ductography, is a mammographic technique that involves injecting a contrast agent into the ducts of the breast to visualize the ductal system. This is particularly useful in lactating women, where the breast is filled with milk and makes it difficult to obtain a clear mammogram. Galactography can help identify abnormalities such as ductal ectasia, intraductal papillomas, or other conditions that may be causing the breast pain.

**Why Each Wrong Option is Incorrect**
**Option A:** Mammography is not the first-line investigation for lactating women, as the breast tissue is filled with milk, making it difficult to obtain a clear image.
**Option B:** Ultrasound may be useful in evaluating the breast, but it is not the first investigation for lactating women with breast pain.
**Option C:** Clinical examination is essential in assessing the severity and characteristics of the pain, but it is not a specific investigation that can help diagnose the underlying cause.

**Clinical Pearl / High-Yield Fact**
It's essential to remember that lactating women with breast pain should be evaluated for signs of mastitis or abscess formation, which can be life-threatening if left untreated.

**Correct Answer: C. Clinical examination. Clinical examination is essential in assessing the severity and characteristics of the pain.**