Computer use does not damage the eyes, but prolonged use can make the eyes tired, blurry, and have a burning feeling. Part of the reason is that the blink rate goes down with prolonged near effort. To help your eyes, take frequent breaks from the computer; close your eyes for a minute or look far into the distance. Drink plenty of water and try to position the computer screen slightly lower than straight ahead, so that your eyes are not wide open as you look at it. The upper lid will come down a bit with the computer screen slightly lowered, and this will decrease the amount of tear evaporation. Anti-glare or anti-reflective glasses may certainly help, depending on your screen and office conditions.
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