I'm sure you've heard this before, but are you sure that the monitor is at 85hz or higher? That will be flicker free, with anything below that being very eye straining (to most at least) And are you trying to run too high of a resolution? something like 1600x1200 wouldn't be a good choice since it will be so small and with a CRT would be blurry and you'll be straining to read the text. If you wear glasses becaus of near sightedness, take them off if possible when at the computer.
Anyway, LCD's generally are better for your eyes and I agree from personal experience. But don't expect miracles if you're on them too much anyway. Just relax, sit a bit back from the screen, and let your eyes take rests. Eat a good diet... excercise.. sounds very cliche but it helps. It's far from optimal to have your eyes in pain, don't let it go too far and listen to your eye doctor.
EDIT: I will second massraptor's advice on brightness control. It helped me a lot in the past, but this lcd I usually use not isn't too bright anyway so I forgot about it.