As a graphic artist of 30+ years and fellow migraine sufferer, good monitors are worth every penny for me. Dealing with a migraine today for that matter.
I use an LG Ultrafine 5K 27” in combination with my 13” MacBook as the secondary screen and this setup has been really good for me. I’ve had larger screens, which are always tempting, but find 27” is the sweet spot. Larger screen means more light and not quite as sharp. Which brings me to the 5K resolution. 4K is good but the 5K really helps me with eye strain and it may not seem like a big deal but it’s made a big difference for me.
Anything is possible. I deal with both but never saw a correlation. The most likely thing could be dehydration which definitely cause migraines for me and also have an impact constipation.
As to constipation, of course try the usual things recommended. What seems to be helping me of late is eating plenty of kimchi which has lots of probiotics and also taking Jarrow Ideal Bowel Support.