Are you worrying about an old monitor you already had for a long time or a new one? Well, if it still hurts your eyes after a month of use, you have a problem. Can't help here.
But if it is your new monitor that bothers you, try using it for a week or so. I recently got a new 21,5" Alienware and the first days it hurt my eyes even after 15 minutes. But after a week of use (and some heavy gaming
) I forgot about all the issues. So sometimes it does take time to get used to a new bigger, brighter screen. Try to play around with brightness also - some monitors come with brightness set at 100 or 70 or 50%, when I need only 20 or 25%. And try turning off dynamic contrast if you have it. My eyes get tired from it for example.