**Core Concept**
Gout is a form of inflammatory arthritis characterized by sudden, recurrent, severe attacks of pain, swelling, redness, and tenderness in the joints, particularly the base of the big toe. It occurs due to elevated levels of uric acid in the blood, leading to its deposition in joints and surrounding tissues.

**Why the Correct Answer is Right**
The patient's presentation is consistent with gout, as it typically involves sudden onset of severe pain, redness, and swelling in one or more joints. The involvement of the big toe is a classic feature of gout. Uric acid crystals deposit in the joint space, triggering an inflammatory response that leads to the characteristic symptoms. This process is mediated by the activation of immune cells, such as macrophages and neutrophils, which release pro-inflammatory cytokines and chemokines.

**Why Each Wrong Option is Incorrect**
**Option A:** Cellulitis is a bacterial skin infection characterized by redness, swelling, and warmth of the affected area. While it can present with similar symptoms to gout, it typically involves a more diffuse area of involvement and is often accompanied by fever and systemic symptoms.

**Option B:** Deep vein thrombosis (DVT) is a blood clot that forms in the deep veins of the legs, often presenting with pain, swelling, and warmth in the affected limb. However, DVT typically involves the entire leg rather than a single joint, and is often associated with risk factors such as immobility, surgery, or cancer.

**Option D:** Polyarteritis nodosa (PAN) is a type of vasculitis that affects medium-sized arteries, leading to inflammation and damage to various organs. While PAN can present with joint pain and swelling, it is typically accompanied by systemic symptoms such as fever, weight loss, and organ dysfunction.

**Clinical Pearl / High-Yield Fact**
When diagnosing gout, it's essential to consider the patient's medical history, including any previous episodes of joint pain or swelling, as well as their diet and lifestyle habits. A high purine intake, obesity, and certain medications can increase the risk of developing gout.

**✓ Correct Answer: C. Gout**