My cat has these weird second eyelids covering half of its eyes... and it is sneezing. The eyes are very watery too. What's wrong? Is it anything serious?
Those are referred to as third eyelids. When those are showing it is an indication your cat is quite sick. With the sneezing and watery eyes you mentioned I would guess that your cat has a very serious respiratory infection and should be seen by a vet as soon as possible. She/he will need antibiotics and the sooner the better.
A vet can tell you what is wrong with an exam, and prescribe appropriate medication.
From your description, I would strongly encourage you to make an apt. for your cat, it's not likely to kick this by itself.
Please come back and let us know how your cat is doing after treatment is begun.
Just make sure your cat continues to eat and drink. If either of these change, you may need to force feed/water or get to an emergency vet in your area.
If you notice your cat is getting congested and having difficulty breathing, you can isolate the cat in a room and start a vaporizer going to help moisten the air and get them breathing easier. If you don't have a vaporizer, get them in the bathroom and turn the shower on as hot as possible and sit with them while the bathroom gets steamy. Once the bathroom is steamed up, turn off the shower and stay in there until the steam dissipates.
If your cat quits eating, a little bit of slightly warmed up canned food or baby food, Stage 2 chicken or turkey baby food WITHOUT onions, might entice the little one to eat something.
Sounds like a URI - Upper Respiratory Infection, otherwise known as a "kitty cold".
Definitely needs a vet looked at him/her and medication ASAP. If you have other cats, keep them separated.
I'm not sure what you can do in the meantime before you get to a vet, but I suggest if the cat is an indoor/outdoor cat, then keep them indoors only, keep an eye on fluid intake, and make sure your kitty is still using the litter tray. And give him/her lots of cuddles - you know how yuck you feel when you have a cold
Try googling for Upper Respiratory Infection in cats to find more useful hints!
Fatcatdude, there are usually animal clinics open on weekends. Google 'animal emergency clinic' in your area and get the cat in today if at all possible.