I think you should see a doctor as well. If your eyes are really dry, they are more susceptible to injury or infection. At least the doctor can suggest a safe long-term remedy, maybe even write you a prescription for something. You might need something stronger than over the counter stuff.
Long-term or continual use of Visine does have a rebound effect -- when you stop using it, your eyes are bloodshot. I don't know how long it would take for them to readjust and stop being bloodshot on your own, but you should stop using it for a while to see!
But see a doctor to rule out infection, as everyone has said.
Something one of the nurses at work told me is helpful for irritated eyes is to take a cup of water and add JUST ONE OR TWO drops of Johnson & Johnson's baby shampoo. Then take a swab (the kind on a wooden stick, not a cotton Q-tip), dip it in the solution, and gently scrub the lower eyelid -- NOT inside where the mucus membrane is but along the lashes where you would put eyeliner if you were lining inside the lashes.
Does that make sense? Anyway, she said it HAS to be Johnson & Johnson's baby shampoo as that is the only one approved as non-irritating and don't use regular cotton swabs because they have lint.
"Tell me, are you incapable of restraining yourself, or do you take pride in being an insufferable know-it-all?"
It seems like you're out of ideas and this may not help at all, but you might just want to try regular old plain saline (contact) solution. I think I read something about the Visine rebound effect too, so saline may help to keep your eyes hydrated while weaning off of the Visine. Saline is a biological buffer and should help restore the balance of fluids and stuff in your eyes, so it's worth a shot. You should get the most plain-jane store brand contact solution there is... it shouldn't have any additives. And if it doesn't help, it's only like 99 cents anyways, so no harm done.