**Core Concept**
The question requires knowledge of the innervation of the anal region, specifically the nerves responsible for transmitting pain from external hemorrhoids. The correct answer involves understanding the anatomy of the pelvic nerves and their distribution to the anal canal.

**Why the Correct Answer is Right**
The inferior rectal nerve is a branch of the pudendal nerve, which arises from the S2-S4 nerve roots. This nerve provides sensory innervation to the external anal sphincter and the perianal skin, including the area affected by external hemorrhoids. The inferior rectal nerve transmits pain from the external anal sphincter and the perianal skin to the spinal cord, where it is processed as pain.

**Why Each Wrong Option is Incorrect**
**Option A:** The hypogastric nerve, also known as the superior hypogastric plexus, is a sympathetic nerve trunk that provides visceral innervation to the pelvic organs, including the rectum. However, it does not provide sensory innervation to the external anal sphincter or the perianal skin.

**Option C:** The pelvic splanchnic nerves (also known as the inferior hypogastric plexus) are parasympathetic nerves that provide visceral innervation to the pelvic organs, including the rectum. They do not provide sensory innervation to the external anal sphincter or the perianal skin.

**Option D:** The sympathetic plexus, also known as the superior hypogastric plexus, is a network of sympathetic nerves that provides visceral innervation to the pelvic organs, including the rectum. However, it does not provide sensory innervation to the external anal sphincter or the perianal skin.

**Clinical Pearl / High-Yield Fact**
It's essential to remember that the inferior rectal nerve provides sensory innervation to the external anal sphincter and the perianal skin, making it the primary nerve responsible for transmitting pain from external hemorrhoids. This knowledge can be useful in diagnosing and managing anal pain.

**✓ Correct Answer: B. Inferior rectal nerve**