Well, of course rubbing eyes can just cause eye stye. First, you should know that a stye is inflammation of the eyelid, and it is usually inside one of the small glands lining the eyelid. And for the causes, in most cases, it is caused by infection from bacteria. So if you rub your eyes with dirty hands, it will just carry bacteria into your eyes, leading to eye infection. At the same time, your eyes will have eye stye. So just stop rubbing your eyes with hands. By the way, according to some researches, eye stye can also lead to redness in the eyes. Also, burning eyes can be possible too.