I have owned only one phone in my life, a Samsung Galaxy on5 bought in August 2016. I could use it 24 h a day until May 2018. I never fully understood why I could not use it anymore without eyestrain afterwards, but I did run an update in correspondence to the onset of the symptoms. Meanwhile that phone died, I tried a few others, last an iPhone 6s, and no way I could use any.
I tested the iPhone 7Plus of a friend and got excruciating, long-lasting pain after seconds of usage. Literally, seconds.
I would not go down the way of trying every possible phone, unless you have time and you can return the phones which do not work (probably many). Where I live, I cannot return, I need to re-sell. Hence, I am going to test a OnePlus 3 with Android Paranoid because according to some users of this forum the OS "behaves" (probably dithers less than others?). I stopped testing other phones because there is something in the technology, common to all the phones, which my eyes cannot cope with, so it is not gonna happen that one phone will magically work. That is just my humble opinion.
If I were you, instead, I would choose to get some therapy, especially if non-invasive: no medicines, no new lens after new lens just for the sake of trying, but plenty of exercises. So far I benefited only from eye push-ups, Tibetan wheel, and else you can find described in dedicated threads. Some are easy, some are best carried out under the guidance of a skilled optometrist.
Vision therapy is not practiced where I currently live, otherwise that would be my first choice, well knowing there are charlatans in that field too, like anywhere else, taking advantage of desperate people.
Meanwhile I would keep an eye on the technology. Hopefully something new will soon come out which solves our problems.