Cervical Radiculopathy: Given the patient's history of cervical arthritis and symptoms of burning and shooting pain in both arms, tingling, and burning in the upper back, especially at night, cervical radiculopathy is a strong consideration. This condition involves nerve root irritation or compression in the cervical spine, which can cause pain, numbness, and tingling in the arms and upper back.

Peripheral Neuropathy: The patient's symptoms of burning and tingling, particularly at night, could also suggest peripheral neuropathy. This condition involves damage to the peripheral nerves and can be caused by various factors, including diabetes, vitamin deficiencies, or certain medications.
Vitamin B12 Deficiency: The patient's complaints of tiredness, sleep disturbance, and weight loss despite increased food intake, along with neurological symptoms, raise the possibility of a vitamin B12 deficiency. Vitamin B12 plays a crucial role in the production of myelin, the fatty substance that surrounds and protects nerve fibers.
Hypothyroidism: Although less directly related to the primary complaint, the patient's symptoms of tiredness, weight loss despite increased appetite, and sleep disturbances could also be indicative of hypothyroidism, a condition where the thyroid gland does not produce enough thyroid hormone.

Spinal Cord Compression: This is a medical emergency that requires immediate attention. Symptoms can include pain, numbness, or weakness in the arms or legs, and bowel or bladder dysfunction. Given the patient's history of cervical arthritis and current symptoms, spinal cord compression is a critical diagnosis not to miss.
Multiple Myeloma: Although less common, multiple myeloma, a type of blood cancer, can cause bone pain, fatigue, and weight loss. It's essential to consider this diagnosis, especially in an elderly patient with unexplained symptoms.
Lymphoma: Similar to multiple myeloma, lymphoma can present with a wide range of symptoms, including pain, fatigue, weight loss, and neurological symptoms if the spine is involved.

Amyloidosis: A group of diseases that result from the abnormal accumulation of amyloid proteins in various tissues of the body. It can cause a variety of symptoms, including neuropathy, but is relatively rare.
Sjögren's Syndrome: An autoimmune disorder that can cause neuropathy among other symptoms. It's less likely but should be considered in the differential diagnosis, especially if other autoimmune symptoms are present.
Porphyria: A group of rare genetic disorders that can cause neurological symptoms, including pain, numbness, and tingling. However, these conditions are very rare and would be considered only if other diagnoses are ruled out and specific indicators are present.