My Cat's Eye Left Is Half Closed, She Has A Discharge From It And Is Sneezing. Does She Have A Cold Or Conjunctivitis?

It does sound like your cat has conjunctivitis as well as an upper respiratory infection.  The best thing to do is seek veterinary medical attention.  The eye should be examined by make sure the cornea is intact and that she does not have an ocular foreign body.  Some upper respiratory infections are mild and self-limiting.  Once nasal discharge develops, if they stop eating and drinking they need to be seen and treated by a veterinarian. 
Encourage her appetite and thirst by offering canned food and flavoring the water if needed with a small amount of tuna juice or milk.
Some shelters offer low cost or income based clincs and some veterinary clinics will do payment plans.

You cat might be suffering from eye infection. It is a very sensitive organ try not to use any thing except water. Just clean them after every hour or so with cold water and your cat will be fine after 5 to 6 days.

Have fun and enjoy blurting :)

Do you see any discharge or drainage? If so, use a cotton ball moistened with warm water (cat temp is about 101.5 -102 so use this as your guide and test against your wrist) and blot along the eye. I would not advise you to rub because a small opening can cause the crusty matter to be pushed in against the eye or get under the closed area of the eyelid and cause more irritation.

If the discharge or drainage is yellowish to greenish, this can indicate an infection. It should be treated by your vet to avoid possible permanent damage to the eye and eye sight.

You can also use a people thermometer (a baby rectal is best but a regular will do) and moisten the tip with oil, insert it gently into the rectum only a small bit (just the silver end) and hold both thermometer and kitten very still for 3 minutes. If the temp reads above 102 you do probably have an infection and should call your vet. If temp reads below 100 degrees in a kitten, it is usually indicates a serious problem and you need to get vet help immediately.

It may be crusted together. Take a warm wet cotton ball and gently wipe her eye from the inside corner out. Do this 3 times a day and see what happens. If it has green or yellow discharge she may have an infection and need to see the vet. Good luck:)