Sean, the rule I work to is if its only a cold, then exercise will help to flush it through. If it is more like flu (temperature, aches, and generally feeling sh*t), then you must rest, otherwise you will lower your immunity and it will just get worse.
Colds and flu are viruses, so no anti-biotics will cure you of them. Taking painkillers and flu remedies during the day only disguise the fact you are unwell, which then make you feel like doing strenuous things, when you should be resting.
To have caught a cold in the first place probably meant you were run down a bit, either from over training/exercising, stress, bad diet, too many late nights, working too hard, or over doing whatever vices you might be involved in.
All you really need now is a nurse to rub some Vic into your chest before going to bed. And if the nurse is called Vic then you are well on your way to recovery.
Anyway, so hope this helps, get well soon mate.