Cervical Radiculopathy: This condition, often resulting from a herniated disc or cervical spondylosis, can cause pain in the arm and leg on one side due to nerve root compression. The pain pattern typically follows a dermatomal distribution, making it a common cause of unilateral arm and leg pain.

Peripheral Neuropathy: Conditions such as diabetic neuropathy or neuropathy due to vitamin deficiencies can cause pain in the limbs, although it's more commonly bilateral. However, asymmetric onset or more severe involvement on one side can occur.
Complex Regional Pain Syndrome (CRPS): This condition can cause severe, burning pain in one limb, often after an injury. While it typically affects one limb, it can sometimes involve both an arm and a leg on the same side, especially if there's a sympathetic component.
Thoracic Outlet Syndrome: Compression of the nerves and/or blood vessels that pass into the thoracic outlet (the space between your collarbone and first rib) can cause pain in the arm and, less commonly, the leg on the same side, especially if there's referred pain.

Spinal Cord Compression: Conditions like spinal stenosis, tumors, or abscesses can compress the spinal cord, leading to pain, weakness, and sensory changes in the limbs. This is a medical emergency requiring prompt intervention.
Stroke or Transient Ischemic Attack (TIA): While more commonly associated with sudden weakness or numbness, pain can occasionally be a presenting symptom of a stroke or TIA, especially if there's involvement of the thalamus or other pain-processing areas of the brain.
Multiple Sclerosis: This autoimmune disease can cause a wide range of neurological symptoms, including pain, due to demyelination in the central nervous system. Unilateral arm and leg pain could be part of the presentation, especially during a relapse.

Syringomyelia: A condition characterized by the formation of a fluid-filled cavity or syrinx within the spinal cord, which can expand and damage the spinal cord from its center, leading to pain and weakness, often in a cape-like distribution but can be unilateral.
Arachnoiditis: Inflammation of the arachnoid membrane surrounding the spinal cord, which can cause severe, stabbing pain, among other symptoms. It's a rare condition but can be caused by infection, trauma, or as a complication of spinal surgery or myelography.
Neoplastic Conditions: Tumors, either primary or metastatic, affecting the spinal cord, nerve roots, or peripheral nerves can cause unilateral arm and leg pain, although these would be less common presentations.