Sinusitis is the most likely and most common cause. That means an inflammation of the lining of the sinus cavities.
Speaking from recent personal experience, sinus pressure due to a recent cold or flu can result in inflammation in your sinuses that causes pain when you move your eyes far side-to-side and up-and-down.
Similarly, headaches can (but aren't necessarily) be associated with sinusitis as well -- most often in the face / around the eyes / in the temples, or even (more strangely, as I've read elsewhere) the top of your head(!?).
Post-nasal drip may also be present (as it is in my case), but again, not necessarily.
You might or might not actually be 'stuffed up' (I'm not ... just drippy.)
The mucus might be greenish if the infection is bad, but -- you guessed it -- not necessarily.
Infected sinuses may also cause you to feel run-down, sick, energyless, almost like you've got a flu ... but again, not necessarily.
The one direct link there relative to a complaint of eye movement pain is the inflammation in the sinuses. Get thee to a doctor. Try breathing steam ... salt-water rinses up into your sinuses while you shower ... humidifying your air ... temporary use of decongestants ... aspirin to diminish the pain and fight the inflammation ... but only the doc can tell you if you have a bacterial infection that will require antibiotics, or if the inflammation is so bad you need a steroidal spray up into your sinuses. Start with the home remedies and go from there.