I haven't used the X for more than a couple of minutes in a store, so I'm not going to comment specifically about it, just state that it uses PWM which precious iPhones (at least in recent years) did not.
I agree that what you experienced sound like possible migraine with aura. I've had it a couple of times and it's a horrible experience. I often get mild symptoms but a couple of times it has built up to a horrible migraine with aura with loss of sight, coordination and speech for a brief moment.
For me, symptoms are triggered by things that flicker. Some fluorescent lights has given me mild discomfort, while computer monitors and LED light bulbs with heavy PWM has given me strong symptoms. It often gets worse when I'm really tired, or getting sick with a cold, am stressed out or something.
Unfortunately OLED displays by their nature use PWM. It's very impractical or maybe even currently impossible to use analog/current dimming since there's no single backlight but rather every sub-pixel is a light source and is adjusted in brightness. This is usually done at around 240 Hz but it varies somewhat from device to device. The iPhone X is pulsed at 240 Hz.
I have also noticed that the sub-pixel arrangement can also have an effect. Pentile caused me some eye strain in the beginning before I got used to it. Some LCDs in phones have also caused me eye strain and dizziness. My HTC desire Z did that in the beginning. No problem with my Nexus 5 or 5X though. The HTC may have used PWM to dim the backlight whereas the Nexuses probably don't. I did have a Galaxy Nexus which did have an AMOLED display, but I don't remember having a problem with that other than some initial eyestrain.
In my opinion it's a shame that most new phones are getting OLED displays, because I see it as a big step back. We have finally had great LCDs in recent years, with flicker free backlights, and now we're getting flicker again with OLED. OLED also has other problems like the blue subpixels degrading faster than the red and green, giving the display a yellow tint over time. It's not obvious, but when putting a new and 2 year old device of the same type it's clearly visible.
Burn-in is another problem which is also an effect of subpixels degrading. Elements that are bright, and especially that have a lot of blue mixed in will cause the screen to age faster locally which will eventually show up as sort of faint ghost-like copy of what used to be displayed there. My Galaxy Nexus had terrible effects of this kind after a year and a half, but I'm sure the panels made today are better in this regard, but I'm still concern what it will look like after 2-3 years.
For those of us who do have a problem with this, OLED is a problem and the industry pushing hard for OLED concerns me. There's soon no good phones without it, TVs and computers will increasingly come with OLED too. I feel like more research on the effects of PWM is needed, both in general and for migraine sufferers.
I know not everyone will understand the problem, but it can be a real hassle to find a TV or phone that doesn't give symptoms, especially since it may not immediately give symptoms. And this is important to understand. It can build up over time for some, until it becomes too much and causes an aura migraine. This may be after a week, or a couple of months. Most likely it will happen after the return window has closed, because that's just the way things tend to work
. Sometimes symptoms are immediate, at which point it's difficult to judge if it's something that need getting used to, or if it will only become worse over time. Other factors can also have a play like I mentioned above. Being extra tired, getting a cold or being stressed out for example. It can be a frustrating and expensive experience to find something that will work.
If you don't have a problem with any of this then congratulations, good for you! I just hope the industry would take this seriously for those of us who do have a problem with it, and launch LCD versions of flagship devices if they have to use OLED at all.