Peripheral Neuropathy: This is the most likely diagnosis due to the common presentation of burning sensations in the feet, often associated with conditions like diabetes. The unilateral presentation could be due to asymmetric nerve damage or a localized process.

Plantar Fasciitis: Inflammation of the plantar fascia can cause a burning sensation in the sole, especially after periods of rest or at the start of the day. The pain is usually localized to the heel but can radiate.
Tarsal Tunnel Syndrome: Compression of the posterior tibial nerve as it travels through the tarsal tunnel can cause burning sensations, numbness, and pain in the sole of the foot.
Vitamin Deficiency (B12, etc.): Deficiencies in certain vitamins, particularly B12, can lead to neuropathic symptoms including burning sensations in the feet.

Deep Vein Thrombosis (DVT): Although less common, DVT can cause pain and swelling in one leg, which might be perceived as a burning sensation in severe cases. Missing this diagnosis can be fatal due to the risk of pulmonary embolism.
Infection (Cellulitis, Abscess): Infections of the skin and soft tissues can cause pain, redness, and swelling, which might be described as a burning sensation. These conditions require prompt antibiotic treatment.
Compartment Syndrome: This is a medical emergency where increased pressure within a muscle compartment can cause severe pain, often described as burning, and can lead to permanent damage if not treated promptly.

Complex Regional Pain Syndrome (CRPS): A chronic pain condition characterized by severe, burning pain at the site of an injury, which can be out of proportion to the severity of the initial injury.
Erythromelalgia: A disorder characterized by burning pain, heat, and redness in the hands and feet, which can be primary or secondary to other conditions like myeloproliferative disorders.
Neoplastic Processes: Rarely, a burning sensation in one foot could be the presenting symptom of a tumor compressing nerves or invading soft tissues.