Eyes have sharp pain when moving them. The pain is in the back of the eyes. Both are sore and no sign of sinus infection.?

Vision/orbit probs. In this situation, it is possible your vision may be straining causing pain over time. However, i would recommend ruling out something more serious with an MRI or ct scan.
Dry eyes. Although there are numerous possible causes of eye pain, the most common and likely is dry eyes. Pain in the eye is poorly localized. It is simple enough to try otc artificial tears 4x/day. If no improvement, you will need to see your doctor.