You'd better not do the exercise any more if you have the stye which may let your stye get serious. You should wait for the recovery of the stye. You need to have the good rest for the eyes. During the exercise, you will get the eyes infection because of the coming bacterium. You'd better wait for the recovery and then do the exercise.
Absolutely you can. Doing exercise when you get eye stye cannot make your condition much worse than before. Eye stye is most possible because of bacteria and virtues infection. Also, rub and scratch eyes may lead to eye stye. When you do exercise, you must be careful to avoid sweating and other foreign matter enter eyes in case further eye infections occur. Plus, you need to pay attention to your personal hygiene and use warm cloth to clean your eyelids and skin around eyes may help with healing your eye stye.
The stye in the eyes is also called blepharitis, is the acute inflammation of glandula sebacea or tarsus. The bacterials and virus get into the opening of glandula sebacea, it may happen by the inflammation of virus from outside environment. Poor personal hygiene and weak healthy person will be easily to get such eyes disease. However, there's no positive connection between the two things of exercise and stye. If you keep an eye to your personal hygiene, as you doing exercise, it will be nothing serious with the eyes disease during the sports. Do not rub your eyes with dirty hands; prevent the sweat get into your eyes when you exercise. As for the way to get rid of it, we could apply partial hot compress, when the fester runs out, the disease will be recovery. Eye drop may help with it also. Please never squeeze the lump, or it will be dangerous to get irritation.