First of all, the direct reason to the pain is the adjacent muscles, because when you are looking around, actually it is your adjacent muscles that are moving. Now, you know there are several possible causes of this eye pain, such as redness, or itching of the eyeball surface, which could be due to orbital pain, allergies or a superficial infection or irritation of the eyes. Then, you can ask help for your eye doctor to text which is the reason causing your eye hurt, which is very significant because the result will determine you how you can cure it. If your eyes get hurt just because of the allergies and superficial infection, you can just ask the doctor give you some simple medication and it can be easily treated. At the same time, if it is caused by the orbital pain, you should go to hospital and need a fully eye exam.
One main possible reason is that your eyes are too dry which is related with the long time work in front of the computers at daytime. Or the too much crying before the sleep may also cause your eyes to feel pain when you wake up in the morning. You'd better go to see the doctor and have a check. If this is not serious, just using the eye drops can help you. If not, you should accept the treatment that the doctor orders.
It can be said, moving eyeball and looking around cannot produce any damage to your eyes. But you are not, it is most likely you are recently with the eye excessive or pay no attention to eye health. Just as you said, you wake up in the morning and have the eyes ache. But, you should not try to open and train your eyes deliberately. Because at this time, your eyes are very fragile, perhaps the blood vessels and nerves have been affected. The most important thing you should do is to relax your eyes. If the symptoms are not frustrated, you should go to see a doctor.