Your wrist could hurt from either poor positioning, compression or overuse. The proper position for your wrist is a flat angle where first knuckle is only slightly higher than the wrist. When using gel rests, it is important that the rest be placed under the palm, not the wrist. The underside of wrist houses nerves which, when compressed, can cause numbness or tingling.
If desk is at correct height, back problems can be the result of poor positioning or prolonged inactivity. Often times, the chair can be retro-fitted with an appropriate lumbar pillow to provide extra support or if the back is adjustable, make sure the curve of chair matches right above your belt line, in the small of your back. Your body is meant to move around so staying in a seated position many hours of the day is very taxing on your spinal joints. You should try and get up every hour just to allow your spine to assume its normal, extended posture.
Eyestrain can be a result of excessive use, vision clarity issues or excessive light. Eyestrain can be manifested by dry, irritated eyes, blurred vision and/or headaches. Your eye muscles are susceptible to overuse just as all other muscles in our body.
Upper shoulder pain is usually the result of improper height of desk or keyboard. If the shoulder hurts within the joint itself, this could be the result of overreaching for mouse or keyboard requiring too much shoulder angulation (forearms turning inwards). Always make sure to keep elbows by your side while using mouse to avoid overreaching. If you are wide-shouldered or have noticed a big inward angle of your forearms while typing, an ergonomic shaped keyboard could improve your alignment.