Ankle Sprain: Given the history of a recent injury (broken right pinky toe) and subsequent development of lateral ankle pain and swelling, an ankle sprain is the most likely diagnosis. The tenderness at the Anterior Talofibular Ligament (ATFL) and Achilles tendon, along with painful walking, supports this diagnosis.

Peroneal Tendinopathy: The pain and swelling on the lateral side of the ankle could also suggest peroneal tendinopathy, especially if the tendons are tender to palpation.
Achilles Tendinopathy: The Achilles tendon tenderness could indicate Achilles tendinopathy, which might have been exacerbated by the recent injury and immobilization in a boot.
Lateral Ankle Impingement: This condition could cause pain and swelling on the lateral side of the ankle, especially if there is a history of ankle sprains or trauma.

Deep Vein Thrombosis (DVT): Although less likely, DVT is a potentially life-threatening condition that could present with swelling and pain in the leg or ankle, especially in an immobilized patient.
Osteomyelitis or Septic Arthritis: Infection in the bone or joint could cause pain, swelling, and tenderness, and is a critical diagnosis not to miss, especially in an elderly patient or one with compromised immune function.
Compartment Syndrome: This is a medical emergency that could cause severe pain, swelling, and tenderness, especially if the patient has been immobilized in a boot.

Stress Fracture: A stress fracture in the ankle or foot could cause pain and tenderness, especially if the patient has been increasing their activity level or has osteoporosis.
Gout or Pseudogout: These conditions could cause sudden onset of pain and swelling in the ankle or foot, although they are less likely given the history of trauma.
Tumor or Cyst: A soft tissue tumor or cyst, such as a ganglion cyst, could cause a painful lump on the lateral side of the ankle, although this is a rare possibility.