I agree when someone comes into the PT clinic with some kind of comminicable illness, I send them home. There is nothing like getting a stomach virus from someone in the gym, having to miss two days work, etc.
As far as congestion. I personally will drink plenty of fluid then do some easy cardio, like spinning on my stationary cycle (at home). This can help break up the congestion and help you breathe better. I usually hit a hot shower immediately after this. You want to avoid dropping your body temp with a cold sweat. So, get rid of the sweaty cloths fast, make sure you are dry and warm afterward.
If you are running a fever don't exercise. Rest, see a Doc.