My problems with LED screens and modern screens are exactly like you've heard here a million times, so I won't bother you with those details. My story is exactly the same.
However, the problem is not related to your eyes, although you will feel eyestrain. The problem is that the screens are causing mild seizure activity in your brain. This is why people often have other symptoms such as brain fog, trouble concentrating, dizziness, increased deja-vu, problems with other light sources, etc. It's also why after prolonged exposure to screens that cause irritation, many people exhibit photo sensitivity similar to forms of epilepsy that sometimes lasts for months. If it was just eyestrain, your eyes would recover in a day or less.
I promise you that if everybody here got an EEG test for epilepsy, many would show a positive test result. This is a different type of seizure and epilepsy so you will most likely have no previous symptoms or signs.
Now while this may sound troubling, it actually has a plus side. If enough people realize these screens are triggering epileptic type responses, the manufactures will have to take it more seriously, as seizure activity in the brain is measurable. If we all continue to call it eyestrain the problem will always be ignored and the only hope of fixing it will be if some new technology just happens to not have this problem. However, it's most likely that newer screens will be even worse as they come out.
So if you are having serious symptoms where even a few moments of screen time causes you problems, you need to schedule an EEG. Tell your doctor you are having mental symptoms when looking at screens and you think it's from the flashing. They will order an EEG.
If the results are positive, the doctor may prescribe anti-seizure medication. I suggest you DO NOT take that route, but the choice is yours.
Bottom line, a good number of people have a very mild epileptic response that only happens when exposed to modern screens. They will have had no other symptoms their entire life, so would never suspect this is the cause.
Also, I believe more people have this issue than even realize it. They just chalk it up as eye strain or maybe they don't need to use screens as much. But if you read Mac forums and other places, this is not that obscure, and I bet 20% of people have this to some degree and just figure it's their eyes.