Can compression of nerves in the thoracic spine cause bowel incontinence and moderate back pain?

Yes and No. Compression of the spinal cord in the thoracic spine can cause bowel incontinence and is a medical emergency. Compressed nerves will not cause incontinence but can result in back pain or pain traveling into the ribs, abdomen or upper leg. Bowel incontinence is the most concerning symptom. Go see you doc.
Thoracic spine. At the level of the thorax, there is spinal cord and if there is bowel incontinence or inability to urinate, immediate medical attention should be sought as these are symptoms of spinal cord compression. It should also be accompanied by weakness and numbness in legs. If the thoracic nerve is only involved, there should be no bowel or bladder symptoms.