what realbrad said is true, but you may also want to try to find a 'flicker free' monitor that uses DC current instead of Pulse Width Modulation to control brightness. PWM has been known to cause eyestrain to some people (such as myself). You may also have to play with the brightness and contrast settings, try tuning them down, some monitors are just way too bright and are meant for very well lit rooms, if you are in a dim to dark room, you may have to adjust brightness/contrast. Also glare is your worst enemy, eliminate glare first.
to answer your question 144hz may cause eyestrain if your monitor was spec'd at 144hz but its more of a "overlocked 144hz" or if your video card/video drivers doesnt properly support it may cause eyestrain due to it fluctuating the 144hz, try settings a lower refresh rate for a few days and see if it helps.
First try to determine what is causing your eyestrain, but don't destroy your eyesight trying to.
-- Yes, PWM flicker can be an eyestrain problem. However, it's often over-blamed / mis-diagnosed (e.g. 50% of the blame is sometimes incorrect). Half of the time, PWM is a red herring for other eyestrain causes. Half of the time, PWM is a genuine cause. Forewarned is forearmed.
-- Excessive brightness can sometimes create more eyestrain than the PWM dimming.
-- Excessively low contrast can sometimes create more eyestrain than the PWM dimming.
-- Bad screen colors / bad color spectrum for LED backlights (excessive amounts of blue), can create more eyestrain than the PWM dimming.
-- If you are often sedate, and are now tracking your eyes more often with the new monitor, you might be over-exercising your eyes. (very rare factor, but leaving no stone unturned). If it happens even just staring at monitor, this almost certainly is not the cause.
-- If you loved CRT's (never got eyestrain with CRT's), if your monitor supports lightboost or similar technology try to enable LightBoost and use LightBoost strobe brightness. Some people (including myself and CallSignVega) get less eyestrain with LightBoost due to lack of motion blur, outweighing the LightBoost flicker. It will help people who preferred the CRT-clarity look, but won't help people who are genuinely flicker-sensitive.
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I would highly advise returning the any monitor that hurts your eyes if you cannot solve the problem; no reason to destroy your eyesight over a monitor that doesn't suite you properly.