Black spots in your eyes are not harmful. They are just a pigmented lesion that is similar to the moles on the skin. The lesion, or nevus, or the black spot in your case, usually appears on the sclera, iris. It is a colored part of the eyes lining the insides of the eyelids as membrane and covering the visible surface of the sclera. It can also be seen on the choroid, and choroidal nevus is seeable only in a specialized lamp light. The black spots are caused by excessive melanocytes which produce pigment. Most people with dark skin are born with the spots. Middle-aged people with fair skin can also have this kind of spots that grow slowly. The spots need no treatment, for most of them are harmless. If your black spots occur to you suddenly, they may indicate a malignant cancer. In this case, the spots can be removed by surgery.
Well, first, I think you need to check your eyes to see if your eyes have been hit. And if your eyes have some hit, it can be normal to have this kind of symptom. And you should know that in some degree, it is a sign of black eye. Of course, it all depends if your eyes are hit and how hard the slap was. Generally speaking, when your eyes are hit, it will make the blood around your eyes flow not so smoothly. And then it will turn black spots in your eyes. For your situation, you can put on ice on your eyes so that it can cool them. And remember that you should do this for several times. Anyway, just be careful about it. And you can also go and see the eye doctor too.
It's very common, there are dead cells banded together which called eye floater. I have floater in my eyes too, it doesn't bother me. Eye floater is caused by the breakdown of collagen or cellular debris. Mostly, people have nearsighted or myopic are more likely to get it.
But if the floater is associated with flashing light, then it may mean something serious, you'd better go see your doctor. Floater can't be removed; actually, unless you are concerned about and pay much attention on it, it's unnoticeable. It may sink to the bottom of your eyes. You have to learn to live with it and don't let it bothers you.
Anyway, you need to have a check on whether it is just a floater. Wish you a good luck!