The thyroxine is not going to affect your vision. Both near- far- sightedness and astigmatism are due to changes in the length of the eye, curvature of the cornea and the human lens getting stiff and rigid. None of these are helped with exercises.
As we all age the eye eventually needs reading glasses (Presbyopia). An exception is near-sighted people that can remove their glasses and read (the myopia acts like a built in reading glass). Computers do NOT damage the eye, they MAY fatigues the eye or make them sore after a long session. (Just like standing on your feet all day makes you tired and want to sit down but standing does not destroy the legs for someone like a saleclerk, that is on their feet all day).
JCH III MD
I don't think that there is any way to eliminate nearsightedness or farsightedness through eye exercises. But you could probably waste a lot of time and money on quackery like the Bates method.