A good portion of dizziness problems comes from issues in the inner ear (vestibular mechanism). So, in addition to checking vision, I would also suggest seeing an ENT and/or Audiologist.
You sound like me, and when I am like that, I go to my chiropractor because my neck is out of alignment. After an adjustment I am OK again until I overdo it once more on the computer.
i would go and have your eyes tested i had the same problem two years ago but since i got my eyes tested and wear my glasses im alot better and if you dont want to wear glasses you could get contacts instead.