Thanks for writing in.
Sun exposure can aggravate pigmentation.Keeping the sunprotection is important to treat hyperpigmentation
. Use sunscreen with SPF 50.
Effective oral and topical medications are now available for Hyperpigmentation around eye.
My advise to you would be to use topical Glyaha cream with good moisturizer.
Take vitamin C
Few treatments like microdermabrasion
and chemical peel can help to dark spots effectively.
Discuss these options with your dermatologist
Hope this helps.