It is in fact quite common to develop pigmentations (eg solar lentigos, melasma, etc) on the face especially for Asian skin types, and from middle age onwards. Other than the usual excessive sun exposure, another reason can be genetic factors as you have pointed out.
It is very encouraging for you to adopt sun protection measures. However still, if your pigmentations keep recurring, it is best to let a doctor help you to manage and hand-hold you to further treat and prevent further recurrence.
Depending on the type and severity of your pigmentations, topical lightening cream alone can help to see good improvement. So you may not need chemical peels or laser treatments at all.
For now, I would recommend you to find an experienced doctor to discuss on the most suitable treatment options for you.
For more information on the treatments of solar lentigo and melasma, you can read more about them in my "Ultimate Guide to Pigmentation Treatment in Singapore".
Hope this helps!
Cheers!
Dr. David Ng CH