This combination of pigmentation on your eyeball and on the skin on and around your eyelid sounds consistent with a diagnosis called oculodermal melanocytosis.
This usually happens in someone of African, Asian or Hispanic descent, but can happen in caucasian individuals.
This is something that should be monitored on a regular basis, at least every year or more often as your ophthalmologist and/or dermatologist recommend. The skin pigmentation can transform into a malignancy and is more likely to occur in a caucasian individual. In addition, approximately 1 in 400 individuals with this develop a malignant melanoma in the colored tissues inside the eye called the uvea.
I think regular follow-up with a dermatologist and an ophthalmologist (oculoplastics specialist or glaucoma specialist) would be warranted.
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My opinion is solely informative and does not constitute a formal medical opinion or recommendation. For a formal medical opinion and/or recommendation you must see an eye doctor.