If your eyes hurt it's causing damage, though perhaps very slight.
Any sort of overuse, over a long period of time will cause your eyes to wear out sooner as you grow older, you'll experience more troubles earlier in life rather than later. I.e. you'll have more difficulty with night vision, night driving, floaters, that sort of thing in the long run, sooner.
So, just don't overdo it, change your habits. Take regular breaks from the screen. You'll be happier for it, rather than getting into a dull grind. The rather hypnotic nature of electronic viewing however discourages it so you have to work on it.
Pain means that's what you're doing is too much. When you're younger you aren't yet familiar with how body parts wear out and never get better. They wear out sooner if you use them poorly, and you get older quicker. Not being able to drive at night as easily because of your night vision getting bad is not small potatoes.
Temperance is a virtue, intemperance a vice, so intemperate use of electronic screens is harmful to your health and to your habits over all. Doing one single thing over a long period of time is not good no matter what it is.
Likely to become more nearsighted sooner too, likely enough.
You're better off than when CRTs were the norm at least, LCDs are easier on the eyes than they were. :)
When you do use a monitor, make sure the room is not dark, but lit instead -- it's important in more ways than one, and a matte rather than glossy screen is easier on the eyes, however nicer the glossies might look.
Also, using monitors over long period of times without break is bad for the mind, as you cultivate a passive mind that takes in and receives whatever is fed it without the necessary discrimination of thought and feeling.
Also, you might want to get your eyes checked, you may need glasses (don't use contacts if possible, they're harder on the eyes), and some glasses can be tinted to help with monitor glare.