Chronic Pain Syndrome: Given the patient's history of multiple gunshot wounds (GSWs) and subsequent surgeries, it is likely that the patient is experiencing chronic pain due to residual tissue damage, nerve damage, or scar tissue formation. The constant throbbing pain reported by the patient is consistent with this diagnosis.

Musculoskeletal Injury: The patient's history of trauma and surgery increases the risk of musculoskeletal injuries, such as tendonitis, ligament sprains, or muscle strains, which could be causing the right leg pain.
Neuropathic Pain: The patient's GSWs and surgeries may have resulted in nerve damage, leading to neuropathic pain characterized by a constant throbbing or burning sensation.
Osteoarthritis: The patient's history of trauma and surgery may have accelerated wear and tear on the joints, leading to osteoarthritis, which could be causing the right leg pain.

Deep Vein Thrombosis (DVT): Although less likely, DVT is a potentially life-threatening condition that requires prompt diagnosis and treatment. The patient's history of surgery and immobility increases the risk of DVT.
Osteomyelitis: The patient's history of GSWs and surgery increases the risk of osteomyelitis, a bone infection that can cause chronic pain and other systemic symptoms.
Compartment Syndrome: This is a rare but potentially life-threatening condition that can occur after trauma or surgery, causing increased pressure within a muscle compartment and leading to nerve and muscle damage.

Complex Regional Pain Syndrome (CRPS): A rare condition characterized by chronic pain, inflammation, and sensitivity in one limb, often occurring after trauma or surgery.
Ehlers-Danlos Syndrome: A rare genetic disorder that affects connective tissue, increasing the risk of musculoskeletal injuries and chronic pain.
Sickle Cell Disease: A rare genetic disorder that can cause chronic pain, including leg pain, due to vaso-occlusive crises.