Peroneal Tendinitis: This condition is characterized by inflammation of the peroneal tendons, which run along the outside of the ankle. The patient's complaint of pain in the "corner" of the ankle, exacerbated by prolonged standing, and severe pain upon rising after rest are consistent with peroneal tendinitis. The temporary relief provided by compression socks also supports this diagnosis, as it can help reduce swelling and provide support to the tendons.

Ankle Osteoarthritis: Given the patient's history of arthritis in the big toe joint, it's plausible that osteoarthritis could be affecting the ankle joint as well, contributing to the pain, especially with prolonged standing and weight-bearing activities.
Peroneal Tenosynovitis: Similar to tendinitis, tenosynovitis involves inflammation of the tendon sheath. The symptoms can be very similar, with pain and swelling along the tendons, exacerbated by activity.
Plantar Fasciitis: Although the pain is described in the "corner" of the ankle, plantar fasciitis could contribute to foot pain that radiates or is referred to the ankle area. The severe pain upon rising after rest is a classic symptom of plantar fasciitis.

Deep Vein Thrombosis (DVT): While less likely given the description of pain exacerbated by standing and relieved by compression socks, DVT is a critical diagnosis not to miss due to its potential for severe complications, including pulmonary embolism. The patient's occupation requiring prolonged standing increases the risk of DVT.
Osteonecrosis of the Talus: This condition, also known as avascular necrosis, can cause severe ankle pain. It might not be the first consideration but is crucial to diagnose early to prevent further bone collapse and arthritis.
Infection or Septic Arthritis: Although the history does not strongly suggest an infectious process, any joint or soft tissue infection in the ankle could present with pain and swelling. This diagnosis is critical to identify promptly to initiate appropriate antibiotic therapy.

Tarsal Tunnel Syndrome: This condition involves compression of the posterior tibial nerve as it travels through the tarsal tunnel on the inner side of the ankle. It could cause pain, numbness, and tingling in the foot and ankle but is less common than other causes of ankle pain.
Gout or Pseudogout: These are forms of arthritis that can cause sudden, severe joint pain. While the big toe is the most common site, they can affect the ankle. The patient's history of arthritis in the big toe joint might suggest a predisposition to these conditions, but the pattern of pain described is not typical for gout or pseudogout.
Stress Fracture: A stress fracture in one of the bones of the ankle or foot could cause pain that worsens with activity. This diagnosis might be considered if the pain is more localized to a specific bone area and if there's a history of increased activity or stress on the ankle.