I used to get something like this, except I described it more like a "burning" behind my eyes. My optometrist recommended reading glasses for computer use. During the day, I wear glasses for nearsightedness, and it turns out that using those while working on a computer was causing a lot of eye strain. I found that reading glasses are actually pretty great -- they force your eyes to focus at a very close range, letting your eyes relax. Since I started wearing them, the burning has gone away. Perhaps you could try something similar.
