A real quick trick, use a nude or off white liner on the inner rims of your eyes to make them appear larger and more open. Either shade will tone out the natural red there and help the whites of eyes look brighter.
Often I prefer using nude as it looks a bit more natural, I like using white for going-out looks or if I'm doing a dark, smokey eye and really want that pop of contrast against black shadow.
Some options include Stila's Kajal Pencil, which is my fave, it's super pigmented, creamy, smooth and easy to apply and long wearing, especially for the inner rim of the eyes (currently out of stock online, but call your local store and see if its there, or even check Stila's webpage, or Ulta, I think they might still carry it):
Tarte EmphasEYES Inner Rim Brightener:
Urban Decay's 24/7 Glide on Pencil in Yeyo (metallic white, so it's not as stark as solid white, has a shimmery effect):
Just do a search on here for "nude eye pencil" and it'll bring up other brands with pencils to offer for a quick, brightening, and enhancing fix.