As a general principle, illness does exempt someone from the Lenten fasting and abstinence requirements. That said, as uncomfortable as a head cold can be, ordinarily it is not a serious illness that requires someone to consume chicken (although it may require one to eat regularly and to drink lots of fluids, so I am not challenging your understanding of the fasting exemption). Unless your doctor specifically states that you must drink chicken soup, perhaps you may wish to try other remedies (e.g., vegetable soup) that would allow you to enter into the spirit of the day in some small way.
