I've not figured out why my eyes hurt from external display and notebook screen use, but what I have found to help on various occasions includes:
- stop using such screens for a while (using the Max or Max2 at such times is unproblematic in my case, but I don't typically use it as an external screen that often -- I end up changing the activity I would have otherwise been involved in)
- sit further away from the screen -- I didn't think this would help and had given up on larger displays, but it turned out to work in my case
- turn down the brightness -- this seems to work on my notebook, where if I turn it up, my eyes start hurting
- use matte screen protector -- this also seems to have helped
- don't use the screen for too long continuously
It appears that different folks have difficulty for different reasons. FWIW, the following site had some info that broadened my horizons:
https://ledstrain.org/
In any case, good luck with finding something to improve your situation.