Plantar Fasciitis: This condition is characterized by pain and swelling on the bottom of the foot, often worse with walking. The intermittent nature of the pain and its location are consistent with plantar fasciitis. The lack of response to ibuprofen and Aleve could be due to the severity of the condition or the need for a more targeted treatment approach.

Peroneal Tendinitis: Inflammation of the peroneal tendons on the side of the foot could cause pain and swelling, especially with activities that involve ankle movement. The pain's location on the side of the foot supports this diagnosis.
Morton's Neuroma: A condition where a nerve in the foot becomes irritated, causing pain between the toes and potentially on the bottom of the foot. The intermittent pain pattern could fit this diagnosis, especially if the pain is more pronounced when walking.
Stress Fracture: A small crack in one of the bones in the foot could cause pain and swelling, especially if the fracture is in a weight-bearing bone. The worsening of pain over time and its location could suggest a stress fracture.

Deep Vein Thrombosis (DVT): Although less common in the foot, DVT could cause swelling and pain. Given the potential severity of DVT, including the risk of pulmonary embolism, it's crucial to consider this diagnosis, especially if there are risk factors such as recent travel, immobility, or family history.
Infection (Cellulitis or Abscess): An infection in the foot could cause pain, swelling, and redness. The severity of the pain and the lack of response to over-the-counter pain medications could indicate an infectious process.
Gout: Despite the patient's statement that they haven't had gout before, it's a condition that should be considered, especially given the acute onset of severe pain. Gout can occur without a previous history and can affect any joint, including those in the foot.

Tarsal Tunnel Syndrome: Similar to carpal tunnel syndrome but affecting the foot, this condition involves compression of the posterior tibial nerve. It could cause pain, numbness, and tingling on the bottom of the foot.
Lisfranc Injury: An injury to the joints or ligaments in the middle of the foot could cause pain and swelling, especially if there was a recent trauma or stress to the foot.
Erythromelalgia: A rare disorder characterized by burning pain, heat, and redness in the feet, which could be considered if other diagnoses are ruled out and the pain pattern is consistent with this condition.