Hi again,
Some news. I recently purchased an old monitor Dell U2413 because I use something similar at work (U3014). The monitor at work causes absolutely no problems to my eyes. My work computer has a Nvidia K620 GPU and the monitor is running on DisplayPort cable. I figured I would search for a similar monitor but 24 inch. So I purchased a used U2413. The difference between U2413 and U3014 seems to be only the panel color depth. The U3014 is using 10bit and the U2413 is using 8bit+frc. Both panels are AH-IPS with GB-r LED backlight.
Anyway, on Windows 10 I don't have the red eye problem anymore. On Linux this combination works: Nvidia Quadro T600 + Dell U2413 + DVI + Nvidia drivers.
I am, however, very confused. I tried the displayport connection first. On Windows there was no problem, but on Linux it seemed that although I would get less eye discomfort, I did feel slight tingling in my eyes. Then I switched to DVI cable and the tingling was gone. I wish I knew what is going on. Maybe Linux developers should start using newer monitors and connections, maybe then they would stumble upon the same problem themselves and perhaps solve it.