Hello, my name is***** and I have over 20 years of experience as a veterinarian. I understand your concern about Katie's left third eyelid being more prominent than usual for the past few days.
The third eyelid is a protective eyelid and can rise up in response to irritation in the eye such as a foreign body, getting an irritant sprayed in her eye, a scratch on the cornea (clear outer part of the eye) or an upper respiratory infection. In these cases you will see a discharge from the eye, clear, yellow or green, you may see redness of the white around the eye and sometimes the kitty will rub the eye or sneeze repeatedly.
The third eyelid can also rise up secondary to a syndrome called Horner's Syndrome. This is secondary to irritation of the nerve that innervates the upper eyelid, some eye muscles as well as the third eyelid. In these cases the eye may look sunken as well and the pupil will be smaller in that eye. Please look at this link for a picture: http://2.bp.blogspot.com/_dhJcewUrnkc/TGVco4_fjhI/AAAAAAAAAkw/2ulqA1t_S9c/s400/cathorner's.jpg
If both eyes were affected it would be more likely that this is secondary to intestinal irritation or parasites. In this case there won't be any discharge, the kitty will be bright and normal otherwise and treating the intestinal upset or parasites will cause the eyelids to return to normal in several week's time.
If your kitty goes outside or comes into contact with other kitties or is from a shelter the two most likely scenarios for her third eyelid to be up consistently would be intestinal parasites or an upper respiratory infection since both are commonly seen in cats, especially those in crowded, shelter situations. If she had both eyes affected and seemed normal otherwise I would try treating her for gastrointestinal parasites and watching her for any other symptoms. In all likelihood if this were related to a respiratory infection or parasites and we treated the parasite then she will be normal in a few week's time.
Since she only has one eye affected this is more likely due to some sort of trauma to her eye, an ear infection or polyp in her inner ear causing inflammation of the nerve or other causes of inflammation to the nerve that controls the third eyelid.
If she doesn't have green or yellow eye discharge, her eye isn't red, and she is eating and drinking normally, and seems bright and alert this isn't an emergency, and having her seen later this week is fine.
Please let me know if you have any further questions.