My axilla and inguinal areas are dark, i went to dermatologist and she gave me a gel formed solution with glycolic and kojic.. can it lighten my skin?

Yes: Kojic acid and glycolic acid are mild acids that are used for peeling and lightening the skin. Since these acids are relatively mild, the lightening will take some time. The alternative would be a chemical peel in the office or laser resurfacing.

Skin Lightening: I would absolutely try it. Kojic acid is an herbal extract which has been shown to help lighten hyperpigmentation (dark areas). Glycolic acid is an exfoliator and anthing that helps the epidermis exfoliate will help get trid of cells that already have excess pigment inside them. Hydroquinone is another skin lightening agent that works well, but some people are allergic to it.