Sweating from exercise might be good because the only way anything can drain out of your lymph nodes is through sweat. At least that's my personal theory.
However if you feel fatigue then don't exercise, you could cause long term problems by exercising with sickness induced fatigue.
Note fatigue is not "cranky and tired": you will know it when it happens. Such as earlier this year I thought I was over my cold and tried to take public transportation to work; I got so tired just walking a few blocks I thought I would pass out. That is fatigue
