It does sound like you have dry eyes, but I would be a little concerned about such a sudden onset. Stop using the Visine right away, because like Chris said it can eventually cause the problem to get worse. Also, it is going to sting because it has preservatives in it and is a very harsh drop. The commercials for the redness reliever drops (if that's the type of Visine that you are using), as well as most of the other Visine drops all say that they are safe to use as often as necessary. But when it becomes necessary for you to use them more than once or twice a day, they can cause side effects and are not good to use. Preservative free artificial tears are the way to go. They come in boxes of individual vials, not bottles. So they don't need preservatives because they are for single uses.
You also need to see an ophthalmologist to figure out the cause and best possible treatment for your new problem. And please, throw out the Visine.

(I made the same mistake when I first started with my dry eye problems, and it made them much worse.)