I used retinol under my left eye and it got dry and dark. Will these side effects go away?

Retinol in high doses can make the skin extra sensitive and causes an intense peeling effect. That is why it's always best to apply the cream in very thin layers and small pea-sized amounts. The pigmentation change is hard to assess without good photos or in-person examination, but it's possible that your under eye skin was left sensitive to pigmentation changes in the sunlight. Moving forward, I strongly advise that you apply SPF 30 lotion daily to your face and neck skin to prevent any further pigmentation changes. In regards to the persistent peeling, use a gentle moisturizer on the skin once or twice daily as needed, I personally like Hyaluronic Acid serums that are helpful in moving water into the skin. This sounds redundant, but drink lots of water! Keeping your body well hydrated is important for maintenance of the healthy skin. Lastly, I want to advise that you seek in-person examination with a Dermatologist or Facial Plastics/Aesthetics office that has thorough knowledge and experience with treatments for hyperpigmented skin. Best, Dr. Anil Shah