When I focus on something close (<6 inches), I start seeing double, is this ok?

Yes. When you focus on something that is that close, your eyes only have the power to maintain that focus for a short period of time depending on your age. Ultimately the object that you are focusing on at near over reaches the limits of your ability to maintain the image in 3 dimensions and it is then that you begin to see double. This is relieved by you moving the object further away once again.