I went to a good optometrist. He found some slight BVD and slight astigmatism in me. Especially in a test that looked like this:

(my eyes, with special polarized glasses, saw the vertical line moved a bit to the left, and not centered on the blank space in the middle)
I showed him this pic which shows how I have a slight "vertically doubled" effect (on high-contrast white-on-black text) (like @bkdo does):

(even when looking with just one eye open)
So he focused on trying to combat this diplopia (double vision) via prism and/or astigmatism lenses. Nothing he did fixed this diplopia so he thought that prism/astigmatism lenses won't help my screen strain.
Maybe my diplopia is a red herring though. (i.e. it may not be the cause of my screen strain).
Can you guys advice? Should I get prism/astigmatic lenses (despite them not fixing my diplopia)?
The other thing I'm worried about is: When I slightly overwork some muscle (eye muscle, leg muscle...), my spasticity (in that part of the body) gets worse permanently. I.e. it doesn't get better afterwards. (the reason is: "chronic withdrawal syndrome" caused by a sharp decreasing of the dose of powerful medications). So if I get prism/astig lenses, and they start "training" my eyes anew, this "training" might overwork the eye muscles, causing a permanent worsening of my condition. What do you think?