I agree with Dr. Humphries, OTC treatment is not recommended without a diagnosis, and applying medications around the eye risks getting a potentially irritating medication into the eye itself. The most likely cause for dark irritated skin around the eye of a puppy would be a skin infection with bacteria, demodectic mange mites, or fungus (ringworm). Your veterinarian can perform skin scrapes to look for infection and mites, +/- ringworm culture if needed and prescribe the appropriate therapy based on test results.
Good luck,
Kimberly Coyner, DVM DACVD
Without seeing this I can't say. However scratching the eye, even the area around the eye, can cause a serious eye injury. Guessing what this is would not be a good idea, hence I would not recommend any OTC meds.
A veterinary exam and proper diagnosis and treatment is needed.