Thanks for the question Mocha.
While I cannot diagnose this over the internet I can talk you through what I would be thinking if I was presented with such a case at my clinic.
Have a look at this image HERE
and see if it is what your cat has ...
If so this is the third eyelid of the cat and is on the inside corner of the cat's eye and is referred to as the nictitating membrane. It is the same membrane you see in the eyes of birds and snakes but people do not have it. Its function is unclear it may act to clean debris off the eye.
In some cats the third eyelid is noticeable but they are perfectly healthy in every other way, in other cats it may be a sign that they are ill in some way but it is not a reliable indicator which type of illness your cat may be suffering from. Of course if your cat is showing other signs of illness you should have it checked out by your vet.
As long as your cat is bright and healthy I would not worry about it, it will most likely go down on its own in a week or so. If it persists longer than that you should have your vet check your cat out.
If I have not answered your question fully enough or if you would like to ask more I will be on line for the next hour or so and I will be pleased to discuss your question further.
Scott Nimmo BVMS