Eye strain after using Ubuntu for some time

One possible cause could be incorrect refresh rate and (or) resolution. This was a generic issue in the time of CRT monitors being, but we could experience similar issues also with the modern monitors. So, find the the monitor's specification and check what are the native values of the refresh rate and the resolution. Or find these values in Windows ^[1]. Then use xrandr to check the current values (the line marked with asterisk *) and compare them with the default ones.

Unfortunately xrandr has really limited functionalities ^{[2] [3]} within Ubuntu 17.10 under Wayland ^[4]. But it will provide enough information.

If this is the problem the next question should be - how do I change these values within the certain Ubuntu version?

If it is 17.10 on Wayland, you may try to find the native values under the menu Displays, as it is shown on the image from the @pomsky's answer. If they don't exist, you could try to follow this answer, where @Panther describes how to generate and enable custom resolution under Wayland.

Another possible way to solve this problem is to run Ubuntu on Xorg, where xrandr will be more useful. Then you could try to use some solution as these suggested here.

You may try two things.

Reduce display brightness

Click on the rightmost corner of the top bar and use the brightness slider to decrease screen's brightness.

Use "Night Light" feature

Go to Settings > Devices > Displays and click on Night Light. You'll be able to turn on a feature which changes screen's colour temperature to a more soothing one.

There is a brilliant piece of software Redshift

for auto screen temperature adjustment. I found it very much relaxing for my eyes, please check this out.

Note: I was not aware of the Ubuntu 17 wayland support, suggest gnome Night light feature instead.