Now is the time to step up your Triluma, or other hydroquinone, or Lumixyl (plant based) and really gob on the sunscreen. A good one that's not chalky but has 18% zinc is the ZinClear SPF 30 by Dermaquest (scroll down on the page to see it).  Or you can layer sunscreens as I do by using the Colorescience powder sunscreen on top of a lotion sunscreen.

See Dr. Irwin's recommendations for layering sunscreens.