Hello!
This is Dr.Klarida Papaqako answering your question.
Permanent
hair removal is a cosmetic treatment of removing hair almost permanently.
You will need 4-8 sessions of 4-6 weeks apart. The skin needs to be not tanned, the hair not removed, shaved or taken off recently.
You can remove the hair also using twisers, depilatory machines or creams.
Although what I would recommend to do first, is to check the skin zone to the
dermatologist. The hair is the skin, around your eyes is not common (except the eyebrows who can be removed by twisers) and it may come from a condition called
Hirsutism, who may come from variations of some hormone levels in the body.
From your description, looks like its hair in not a common place. So doing those labs and ruling out you don't need a medical treatment for it, other then cosmetic, should be the first step.
Hope this helps,
Regards.