Does spinal stenosis cause pain in the arms and shoulders?

It can: Stenosis of the cervical spine (in the neck) can cause spinal cord or nerve root compression which in turn can cause pain in the arms and shoulders.

Spinal stenosis: If it is lumbar and not cervical spinal stenosis pain in the upper body would be very uncommon, much more common in the legs and feet if it is lumbar stenosis.

Potentially: Stenosis in the neck can definitely cause pai in the arms and shoulders, there can be other causes as well,