Cellulitis with secondary lymphedema or dependent edema: This is the most straightforward explanation, where the cellulitis in the right leg could lead to swelling due to infection and inflammation, and the left hand swelling could be due to dependent edema from prolonged periods of sitting or lying down, or secondary lymphedema if the infection has affected lymphatic drainage.

Deep Vein Thrombosis (DVT): The pain and swelling in the right leg could be indicative of DVT, especially if there's a history of recent immobility, surgery, or cancer. The left hand swelling might be unrelated or could be due to a separate DVT, though this would be less common.
Infectious endocarditis with septic emboli: Although less common, this could explain both the cellulitis (if it's a result of a septic embolus) and the swelling in the other hand (if there's another embolic event).
Lymphangitis or lymphadenitis: Infection spreading through the lymphatic system could cause swelling and pain in both the right leg and the left hand, though this would typically be accompanied by other symptoms like red streaks or swollen lymph nodes.

Necrotizing fasciitis: A severe infection that could start as cellulitis but rapidly progresses, requiring immediate surgical intervention. The presence of severe pain out of proportion to the physical findings is a red flag.
Sepsis: Especially if the patient shows signs of systemic infection such as fever, tachycardia, tachypnea, or altered mental status. Sepsis can lead to multi-organ failure and death if not promptly treated.
Compartment syndrome: Could be a complication of severe infection or swelling, leading to increased pressure within a muscle compartment, which is an emergency requiring immediate intervention.

Erythema elevatum diutinum: A rare skin condition characterized by recurrent, tender, red-purple lesions that can mimic cellulitis and can be associated with various systemic diseases.
Sweet syndrome (acute febrile neutrophilic dermatosis): Characterized by fever, leukocytosis, and tender, erythematous skin lesions, which could be confused with cellulitis.
Kikuchi-Fujimoto disease: A rare, self-limiting condition that can cause lymphadenopathy and might be associated with skin manifestations, though it's more commonly associated with cervical lymphadenopathy and fever.