My cats Third Eyelid showing ?

My female moggy cat Carlton has been showing the third eye for 2weeks, I've been on holiday and come back to her in this state.
She's pregnant around 4weeks or so, she's acting completely normal, eating as usual, playing/fighting, grooming, wanting to go outside etc just wondering what it could be? I have an appointment with the vets but soonest I could be fitted in is in a week, she won't die in that time will she?! I know there's loads of reasons as to why the third eye would should but she's not acting sick at all... It's confusing to be honest lol

Cats are experts in hiding pain and illness- just because she's not acting sick doesn't mean there isn't something else going on.

You are right that a visible third eyelid can be caused by a whole host of things. It can be as simple as stress to as serious as dehydration, worms, a respiratory infection, or a herpes virus. Will she die from it? There is really no way to know without knowing what is causing it. A small case of dehydration can become deadly if not remedied within a matter of days. The bottom line is there is no way around a vet visit and, given her pregnant status, you really need to go sooner rather than later. 

I would call and see if you can get in with another vet at the practice. Or, think about seeing another vet who you can get in with sooner. It's ultimately your choice but I would not wait another week, especially considering it has been going on for awhile. If it is some sort of infection you want to treat it before the kittens come. Otherwise, there is a high probability of her spreading it to them. In that situation something simple can become life threatening very quickly- not to mention extremely costly. I would also take a stool sample when you do go so they can check for worms and parasites. It's easier to take with you than having to go back or worse, having them force a sample! 

I also just want to comment on her pregnant status. I know she wants to go out but it's critical that from now until the time she is spayed she is indoor only. You don't want to risk her picking up any other infections or chance her having her kittens outside where you can't find them. Start getting her used to the idea now by keeping her inside 24/7. And, remember that she can go into heat again quickly after giving birth so until she is spayed she must stay inside and away from any intact males. She will do everything in her power to get out so confining her to one room away from an outside door is usually the best way to go. Not only does it ensure she doesn't sneak out, but gives her the privacy that she needs to raise her kittens. 

Good luck getting her to a vet sometime this week and check out the Pregnant Cats and Kittens section to prepare yourself on what is to come!