One of the main reasons that your body aches when you are sick, like with a cold is that your body's immmune system is producing plenty of anti-bodies.
These anti-bodies also produce histamines which dilates (widens) blood vessel. These chemicals ae released into your blood stream and end up in your muscles.
One reason you ache is that these chemicals are sometimes triggering nerves in your body, your muscles and cause them contract a little more than usual. This constant contraction can sometimes cause that feeling of an ache.
If your muscles are contracting alot they can produce lactic acid, this lactic acid can produce an aching effect by trigger pain receptors. This is similar to what you feel in your legs after you have run a sprint.
Types of pain receptors (PDF, technical notes, Texas A&M Univeristy, S.E Reichman)