Please don't take any meds for cold and fever. Anything that goes in your stomach your body prepares for digestion and whole cycle starts again. You were in Ketosis and by taking anything accept for water you are going into digestion mode. Cold and fever are also considered detox symptoms.
Staying warm and resting is best way to get rid of the cold. You may want to try external use of Vicks or tiger balm on your chest.