For specifics, you should probably talk to your eye doctor, but on general, to prevent eye strain on the computer there's the 20-20-20 rule:

Every 20 minutes look at something 20 feet (6m) away for 20 seconds.

That's your eye's resting focusing distance. Doing this should allow it to relax.

You might also need to get your prescription checked. Sometimes it's off by enough to cause eye strain, but not so much that you'll notice it.

Hi. I had my lens removed from my left eye as a very young child due to a cataract after cancer treatment and my cornea is scarred from chronic dry eye caused by radiation. My right eye was removed at 2 mos old. Get your eye checked. You shouldn't be straining so much. I switched to progressive lenses which helped quite a bit at getting the sweet spot for computer work at a natural place. Make sure you're keeping your eye moist or you'll have a lot of problems with the light from a monitor. If you can occasionally look away at something green, that might also help your eye relax. I've used tinted glasses over my prescription glasses when necessary, but it's not ideal to work with every day, especially if you need an unfiltered look at similar colors.