Fibromyalgia: This condition is characterized by widespread musculoskeletal pain accompanied by fatigue, sleep, memory, and mood issues. The burning and squeezing sensory pain in both legs and the right shoulder, along with fatigue and painless muscle spasms, align with the symptoms of fibromyalgia.

Peripheral Neuropathy: This condition can cause burning pain, typically in the feet and hands, but can also affect other areas. It could explain the burning sensation in the legs and potentially the shoulder if the neuropathy is widespread.
Musculoskeletal Strain or Overuse: Repeated strain or overuse of muscles can lead to pain, fatigue, and muscle spasms. This could be a contributing factor, especially if the patient has recently increased physical activity or has a job that involves repetitive movements.
Chronic Fatigue Syndrome (Myalgic Encephalomyelitis): Characterized by extreme fatigue that doesn't improve with rest and worsens with physical or mental activity. While it primarily involves fatigue, it can also include muscle pain and spasms.

Multiple Sclerosis (MS): An autoimmune disease that affects the brain and spinal cord, leading to a wide range of potential symptoms, including pain, fatigue, and muscle spasms. MS can present with almost any neurological symptom, making it a critical diagnosis not to miss.
Lupus: A chronic autoimmune disease that can affect various parts of the body, including the skin, joints, kidneys, brain, and other organs. It can cause a wide range of symptoms, including joint pain, muscle pain, and fatigue.
Vitamin Deficiencies (e.g., Vitamin B12 Deficiency): Certain vitamin deficiencies can cause neurological symptoms, including pain, fatigue, and muscle weakness. These deficiencies are treatable and thus important to diagnose.

Complex Regional Pain Syndrome (CRPS): A condition characterized by persistent burning pain and inflammation, usually after an injury. It's rare and typically affects one limb after an injury or trauma.
Ehlers-Danlos Syndrome: A group of disorders that affect connective tissues supporting the skin, bones, blood vessels, and many other organs and tissues. While it can cause joint pain and fatigue, it's less likely to cause the specific combination of symptoms described.
Mitochondrial Myopathies: A group of disorders caused by mitochondrial dysfunction, leading to muscle weakness and other symptoms. These conditions are rare and might present with a combination of muscle pain, fatigue, and other systemic symptoms.