If anyone stares at a screen of any type for too long, their eyes will feel like they are burning. Your computer is most likely an LED backlit LCD screen which if not too expensive may have a higher then normal blue component to the spectrum as it goes through many glass interfaces before it ever hits your eyes.
I once designed a home-built projector TV system that used a laptop LCD screen . . . and you'd be amazed at how much light is lost before it ever leaves the screen from the back light. I started with a spherically mirrored 45,000 lumen light source, having tossed out the laptops original LED light source. . . and wound up with only 3200 lumen at the screen's surface, all due to light loss from going through multiple glass surfaces and the coatings on them to filter out exactly what you are complaining about. I did quite a bit of study on it.
I'm an Apple user and am a bit prejudiced. . . but you might see why with the following chart. Your typical White LED back light used most computer monitors is on the left. . . but Apple uses LED back lights that are different which produce the spectra on the right, that are much easier on the eyes for long periods of use.
Higher priced, higher quality LED backlit monitors generally use the Red-Green phosphor approach to backlighting which gives a far better color gamut than the "pure white" (read blue shifted" LED backlit monitors.