Thanks for the questionCustomer
While I cannot diagnose your cat's disease over the internet I can tell you the following :
1. Cats do not suffer from colds and sneeze in the same way as people do, however the most likely condition your cat would be suffering from is cat flu. The problem you face on the home remedy front is that the human over the counter cold remedies often contain anti-inflammatory drugs such as aspirin and paracetamol which can be very toxic to cats so you should avoid all over the counter remedies.
This is an upper respiratory tract viral disease which is often endemic in animal shelters, boarding catteries or places where there are stray cats like colonies of cats which live round farms or stables but household cats can get it as well.
Unfortunately there is very little you can do for your cat on a home treatment basis, the best plan is to get a vet involved. You see this is a viral disease for which there is no direct treatment and it will run its course depending on the severity of the infection and the state of your cat's immune system. Some cats recover quickly, others do not do so well and develop a chronic disease, a small percentage may die.
2. The symptoms you would expect to see would be some or all of the following : Runny eyes, a nasal discharge, coughing and sneezing, some cats run a temperature and then stop eating or drinking and become lethargic others can be quite bright and only suffer minor symptoms as the disease runs it course.
3. The treatment would normally include oral antibiotics, antibiotic eye drops if necessary and a good standard of nursing care. This may prevent secondary infections but it will not affect the course of the viral disease so all you can do is hope for the best.
Here is a very good link on the subject so you can research it more : LINK
If I have not covered your question fully enough or you would like to ask more I will be online for the next hour or so and I will be at your disposal.
Scott Nimmo BVMS MRCVS