PL said
For about a month now, whenever I blink, I see this black spot float across my right eye....and it's weird that it's only on my right eye and it doesn't happen every time I blink.
Chances are it's just a floater, which is common and natural. If you start getting flashes of light as well, call an Optometrist as soon as possible.
Lil Me has good advice on the Ophthalmologist, but the waiting period to get in to see him on a non-emerg basis could be quite long.