No, I do not think it is ok for you to wear eye makeup to cover stye around eyes because eye makeup can prevent you from recovering, or even make your condition worse if you do not pay attention to the eye hygiene. You can apply warm compresses over your affected area, which will help drain away the fluids trapped inside the stye. And do not wear contact lenses if you are myopia with stye around eyes. Do not squeeze or press the stye, otherwise, it can be worsened.
No, it is not ok for you to wear the eye makeup when you have the stye around your eyes because of the maybe coming bacterium in your eyes. You'd better not wear the contact lenses, neither. You should take some eye drops to get rid of the bacterium and make the eyes keep moisture. You should protect your eyes carefully.
Ok, it seems that there is something wrong with your eyes, and as you can see, a stye is one of the infections of your eyes. And a stye could give rise to some more serious problems if not treated on time. For now, you must try to cure it before things get worse, some infections could be given by it. Just try to see a doctor and try to get some eye drops and anti inflammation drugs to deal with the problem. For makeup is irritative and may make the situation worse.