I have tried a lot of LED bulbs, I have a box full of them. I made sure to select only ones that have very low flicker or were advertised as "flicker free" (yet they do flicker). But they all cause eye strain and headaches. I have hopes for "violet/purple chip" LEDs, as their spectrum is different, but it seems they aren't available anywhere for end customers.
For now I recommend stockpiling classic incandescent bulbs, if you can still buy them.