I usually take it easy the first few days of illness and skip the daily gym and won't resume if still feeling feverish. I don't think it's ever a good idea to exercise with fever and illness-related aches and pains. Non-severe head cold is probably ok, chest congestion is ok if it doesn't make you easily short of breath. Often, once the acute illness is gone, you are left with a chronic cough and chest congestion that can last weeks, and it is ok to be exercising during this time, again provided you do not easily become short of breath. People are very often incorrectly diagnosed with 'mild pneumonia' or a 'sinus infection' and started inappropriately on antibiotics for their viral infection (which is not treatable with antibiotics) which to their suprise seems not to get better on the antibiotics -- and they are correct!!
Having said all that, if there is any question in your mind whether you have something more than a routine viral upper respiratory infection, you should go see your doctor. I would tell you to make it very clear to your doctor that you do not want to be put on antibiotics if he/she truly believes your illness is viral in origin and not bacterial. In doing this, hopefully you can avoid having yourself unecessarily put on antibiotics (which have their own potentially serious side effects). FYI -- Most of the doctors I have worked with think that patients are only happy if they leave the office with an antibiotic prescription. I don't believe this is really the case and most patients would prefer an honest opinion and it is part of a physician's role to educate patients about illness and proper treatment. Of course, there are a few patients who want nothing less than antibiotics at the first sign of a sniffle and cannot be educated -- try not to be one of those!
Hope that all helps
Glen (M.D.)