By all means, check with your veterinary about those cold symptoms. We've had feline upper respiratory illness (aka 'kitty cold') bouncing around our shelter since about Christmas. We keep the affected cats in one room, and isolated from the others. It seems to take a couple of weeks with treatment to run its course. Without treatment, it is like whatever bug is going around at a child's school. Eventually, everyone gets it, at least once.

Also, without treatment, your cat may become dehydrated (in some cases the cat does not want to eat or drink), and need intravenous fluids, and/or force feeding. Nether is pleasant to do, as the cat may not want to cooperate with the caregiver.