I face the same problem, there is a dark circle around my eyes, but it's not an eye bag. I'm suspicious it's because I'm thin, the structure of my skull makes flesh around my eyes sunken. Compressing doesn't seem to make any difference. But I do make some precaution:

• I'm using glasses with Bluray filter when using the computer.
• I always sit down/manage the right position when using the computer. I avoid using it by lying in bed.
• Drink enough water.
• Reduce the white spot/brightness of my gadget.
• I am not too close when watching tv.
• Always blinking and see the green leave of a tree, or something far, like a scenery, once in a while.