About the inner eyelid thing...
Perhaps it only kicks in during emergencies, where a sudden burst of light occurs (such as when Spock goes into the chamber in "Operation: Annihilate!"). Normal, everyday exposure to bright environments might not be enough for the inner eyelid to come into play. So, in-universe, that's probably why Oh was wearing the sunglasses. Or she could have suffered from some other affliction which caused her to be sensitive to light.
And remember, when the inner eyelid DOES activate, it will completely obscure all vision. That's why Spock thought he was blind.