I'm not a doctor... but.. the rash could be from the antibiotic, it's been known to happen, it also could have been from the sickness and as a result of the bugs dying. If you child's condition changes or the fever pops up, you should call the doctor and have him/her looked at.
Do you think that he is allergic to the cold? I am and can actually break out in hives from it. Since he is on an antibiotic it would probably be wise to check with your doctor to make sure it is not due to the drug.