When I have a cold, I put on my warmest clothes (winter coat, even), get a cup of hot tea, a few glasses of hot water and a bowl of the spiciest chili I can handle and sit down in front of the radiator. It brings your body heat up quickly and basically induces a temporary fever. I stay like that until I'm super-sweaty, and then cool myself off again. Fevers are our bodies' natural way of killing viruses, this is simply my strategy to help that process along.
Garlic & cayenne at the onset - like in your chili- definitely helps.
Thyme tea once a day and onion soup are also good. Kale and broccoli have natural sulphur which also helps (eat these regularly so you don't GET a cold!)
One of the problems I found when I was suffering from colds and allergies often was that my system was just too overloaded. I started paying attention to things like the lymph, liver, and kidneys. If they can't process out the 'yucky' stuff that's usually when I would get ill. I found Hannah Kroeger's books
http://www.peacefulmeadowretreat.com/index.asp?cat=166200 had some great home remedies to help keep your 'system' clear and ideas for things to do when you are ill.