Nothing strange for your case. However the reason is not directly connected with eyes and throwing up, the reason may be anemia or hypoglycemia.
Your body must be bent, and your face must toward the ground, this whole pose would make you lack of oxygen. Especially when you are throwing up, the moment which means you are uncomfortable.
I suggest you to drink a cup of milk or some water with sugar, or a piece of chocolate may also be helpful.
There must be some problems for your eyes. Your eyes may get the infection by the unconscious coming bacterium. In the normal condition, we will not see stars when we throw up. You'd better go to the hospital to have a full check on the eyes. If there is something wrong with the eyes, you should accept the treatment as soon as possible and they will get recovery soon.
Well, as a matter of fact, sometimes we ordinary people do throw up because of some reasons. And generally speaking, your situation is quite common, we often experience it. However, we need to be careful, because sometimes it is resulted from cerebrovascular disease and could be a sign of it. So I advise that you go through a overall medical examination to see where went wrong.