The treatment of dark circles
lies in solving the underlying cause. Periorbital melanosis
or dark circles have variable causes like chronic disesase(iron deficiency
, thyroid disorder
, atopy), lifestyle factors(stress, anxiety,long waking hours , use of laptops, vision strain), hereditary and localised factors (thin under eye skin along with micro leaks of blood through underlying fineblood vessels). The treatment involves lifestyle modification that is improving your sleep pattern, treating the underlying disease that is anemia or thyroid disorder and use of various topical depigmentary under eye creams. Also peels specifically meant for thin undereye skin and mesotherapy sessions could be used.
The treatment suggested by your doctor is fine and you can initially begin with the same. Sunban cream is a sunscrean and ban a tan cream is a mild depigmentary cream. Ahaglow is a mild face wash with glycolic acid
as such not having any direct role in treatment of dark circles. Dark circles take a long time to respond. So a lot of patience and compliance is required from your side. Hope that answers your query.