Cellulitis: This is a common cause of acute foot swelling, especially in the elderly. The lack of acute trauma and the age of the patient make cellulitis a likely diagnosis due to its prevalence and the increased susceptibility of elderly individuals to skin infections.

Deep Vein Thrombosis (DVT): Although less common than cellulitis, DVT is a plausible cause of acute limb swelling without trauma, especially in an elderly patient who may have risk factors such as immobility, previous DVT, or cancer.
Gout: Acute gouty arthritis can cause rapid swelling of a single foot or joint, and while it's more commonly associated with the big toe, it can affect any joint. The patient's age and potential for dietary or metabolic predispositions make gout a consideration.
Lymphedema: If the patient has a history of cancer, surgery, or radiation therapy, lymphedema could be a cause of unilateral foot swelling. However, its onset is typically more gradual.

Compartment Syndrome: Although less likely without trauma, compartment syndrome is a medical emergency that can result from any condition causing increased pressure within the compartments of the foot, leading to severe pain, swelling, and potentially permanent damage if not promptly treated.
Septic Arthritis: An infection within a joint, which can occur without a clear source of infection and requires urgent diagnosis and treatment to prevent joint destruction.
Osteomyelitis: A bone infection that can cause swelling, pain, and redness, often without a clear history of trauma, and can be devastating if not treated promptly.

Erythromelalgia: A rare disorder characterized by burning pain, heat, and redness in the hands and feet, which could potentially cause swelling.
Complex Regional Pain Syndrome (CRPS): A condition characterized by intense burning or aching pain in the hands or feet after an injury or trauma, which can also lead to swelling, although its onset typically follows a traumatic event.
Sarcoidosis: A systemic disease that can cause swelling in the feet among other symptoms, though it's less common and would typically be accompanied by other systemic signs.