Why do I get styes around my eyes?

Blocked glands. You likely have a skin condition which is leading to blockages of the glands in the eyelids (blepharitis). These blockages lead to the styes that you see. An ophthalmologist would be able to tell you if your eyelids have any tendency toward getting these styes, and offer you specific suggestions. Some people benefit from chronic lid hygeine or even oral medicines to prevent chronic styes.