I was given tretinoin 0.025% for suspected hyperpigmentation under my eyes. what adverse side effects are there using it on such a sensitive area?

You can check the : Side effect profile of tretinoin on this link. Best wishes! http://www.Drugs.Com/sfx/tretinoin-side-effects.Html.

Inflammation: Generally speaking retin- a is not typically used around the eyes due to sensitivity manifested by marked inflammation (redness, swelling) . When used for hyperpigmentation it is commonly combined with a steroid cream and/or hydroquinone and/or kojic acid.