**Core Concept**
Erythema nodosum is a type of skin inflammation that occurs due to a hypersensitivity reaction in the subcutaneous fat, often associated with various systemic diseases, including ulcerative colitis. It presents as tender nodules or plaques, typically on the lower extremities, but can also occur on the face in rare cases.

**Why the Correct Answer is Right**
The patient's symptoms of erythema nodosum, particularly the appearance of a lesion on the cheek, suggest a diagnosis of pyoderma gangrenosum. Pyoderma gangrenosum is a rare skin condition characterized by the development of painful ulcers, often in association with systemic diseases such as ulcerative colitis. The lesion's response to potassium iodide treatment supports this diagnosis, as potassium iodide is sometimes used as a treatment for pyoderma gangrenosum. The exact mechanism of potassium iodide in treating pyoderma gangrenosum is unclear, but it is thought to involve the reduction of inflammation and the promotion of wound healing.

**Why Each Wrong Option is Incorrect**
* **Option A:** Erythema nodosum is a possible diagnosis, but it typically presents on the lower extremities, and the involvement of the cheek is less common. Additionally, the response to potassium iodide treatment is not typical for erythema nodosum.
* **Option B:** None provided, skipping to Option C.

**Why Each Wrong Option is Incorrect (continued)**
* **Option C:** Ulcerative colitis is a systemic disease associated with various extraintestinal manifestations, including erythema nodosum, but the presence of a skin lesion on the cheek and its response to potassium iodide treatment are not characteristic of ulcerative colitis alone.
* **Option D:** None provided.

**Clinical Pearl / High-Yield Fact**
It is essential to recognize that pyoderma gangrenosum can be a challenging diagnosis to make, and a high index of suspicion is required, particularly in patients with a history of systemic diseases like ulcerative colitis. The response to potassium iodide treatment can be a helpful clue in making this diagnosis.

**Correct Answer:** C.