So after posting in health forum about blue-light intensity being a possible cause, I tried to find ways how to measure it. Unfortunately professional spectrometers, even the basic ones, are incredibly expensive (1000 dollars and more). I have found a way to build an amateur spectroscope, that does not measure any values, but shows the white light dispersed into separate colors. With the help of a proper angle encasement and a full CD/DVD, you can construct a really basic light dispersion tool. Bad quality, but nice start.
I have tested it on my ihone SE that gives me the issues and then one iphone 7 that does not seem to, the results are attached. You can clearly see, even with this bad quality images, that there is a difference between these two backlights. Especially that dark band between the reds, and more separation, on the iphone 7.
The iphone SE already has a blue light filter attached, but it does not help much, just postpones the migraine to about one hour of use. Iphone 7 has only clear safety filter.
Also, seeing it in real life and observing only the blue part of the banding, the one on SE seems fuzzy and impossible to focus on, while the on on the 7 more sharp and clear. Maybe the images can somehow also convey this.