I'll tell you - I thought at first it was my TMJ (I have very mild - wear a nightguard but otherwise have no issues) or related to my Tinnitus (both of these involve inflammation in the temple area) but the timelines don't track. I started wearing a nightguard because my jaw really ached in late 2011. I didn't have a problem with monitors until nearly a year later. The tinnitus has been an issue for nearly 20 years, certainly unrelated.
The first thing I noticed I couldn't look at was Macs. Specifically Macbooks with newer ATI chips in them. 2010/2011 models with GeForce in them were fine. 2011/2012 models switched over to ATI Radeon and they were pretty much unusable.
After that I switched jobs, and noticed that some monitors were harsher than others. But I had tried to "force" myself to get through the Macbook issue, and tried to work under the REALLY BAD fluorescent lighting at work, and just couldn't do it. Bear in mind - I was using a 2012 model Lenovo X220 with an LED backlight at the time in a darkened room as my "safe system", so it's not anything intrinsically to do with all LED's.
I was also driving long hours with an eyeglasses prescription that needed updating - my new job required me to drive 1.5-2 hours each way, always into the sun (east in the morning, west in the evening) and by the time I got home I was really burned out.
This caused me to have a massive anxiety outbreak, I was having anxiety attacks pretty regularly at this time which CERTAINLY didn't help.
Known good systems at that point were breaking down. My TV? Unwatchable. XBox 360? Unusable. Anything that required me to focus on a screen was simply out of the question. Store lighting was bad. I was in a really low place, spending most of my time in the dark away from screens.
But there's hope - I'm 1000 times better now, in spite of using a much wider variety of screens! I have relatively recent laptops I can use (my primary work laptop is a 2015 Dell XPS), I can use relatively recent PC's (the 2015 Windows 10 LTSB with a GeForce 970 First Edition is not a bad system under any circumstances), the only remaining issue is my phone.
There are still bad things - the supermarket put in a ton of LED lighting for the checkout aisles... and then took it out because people complained. Vending machine lighting is often LED's now, harsh and horrid. The nearby Wal-Mart put in high-intensity fluorescents above their produce area, and I have to rush to get my lemons and broccoli now lest I get burned out...
But in general I can function. For how long? Not sure. Hopefully long enough for a cure.