Cauda Equina Syndrome: This condition is characterized by compression or damage to the cauda equina (a bundle of spinal nerves and spinal nerve roots), which can cause back pain, radiculopathy (nerve root pain), weakness, and bowel/bladder dysfunction. The patient's symptoms of back pain radiating to the shoulder, progressive arm weakness, hamstring tightening, and associated gastrointestinal symptoms (nausea, diarrhea) are consistent with this diagnosis. The acute onset and rapid progression of symptoms, including the inability to ambulate, further support this diagnosis.

Spinal Cord Infarction: This is a condition where the blood supply to the spinal cord is interrupted, leading to damage or infarction of the spinal cord tissue. Symptoms can include sudden onset of back pain, weakness, and sensory loss, which align with the patient's presentation.
Spinal Epidural Abscess: Although less likely given the absence of fever, this condition involves an infection in the epidural space surrounding the spinal cord, which can cause back pain, weakness, and neurological deficits. The patient's nausea and diarrhea could be non-specific symptoms associated with infection.
Herniated Disk with Neurological Compromise: A herniated disk can compress spinal nerves, leading to back pain, radiculopathy, and weakness. The severity of the patient's symptoms, including significant arm weakness and hamstring tightening, suggests a substantial neurological compromise.

Spinal Cord Compression due to Tumor: This is a critical diagnosis to consider, as it can present with back pain, weakness, and neurological deficits similar to those described by the patient. Prompt diagnosis and treatment are essential to prevent permanent neurological damage.
Aortic Dissection: Although the patient denies chest pain or shortness of breath, aortic dissection can sometimes present atypically, especially in women. Back pain and neurological symptoms can occur if the dissection involves the aorta's branches that supply the spinal cord.
Infectious Meningitis: Given the acute onset of symptoms and the presence of nausea and diarrhea, infectious meningitis must be considered, especially if there's any suspicion of fever or recent illness, despite the patient's denial.

Transverse Myelitis: This is an inflammation of the spinal cord that can cause back pain, weakness, sensory loss, and bowel/bladder dysfunction. It is less common and can be associated with various conditions, including autoimmune diseases and infections.
Neurosarcoidosis: A rare condition where sarcoidosis affects the nervous system, potentially causing back pain, weakness, and neurological deficits. This diagnosis would be considered if other more common causes are ruled out and there are supporting findings suggestive of sarcoidosis.