The warm natural flavours of a nice cup of tea can do wonders for a cold or flu. The nutrients in the leaves help to quicken your healing process and the smooth texture of the tea helps to de-clutter that mucus flooded throat.
A healthy Green tea is recommended for its antioxidant value, maybe try a super cup of Matcha. Ginger tea is also great for upset stomachs and Peppermint tea helps soothe the throat and freshen the sicky breath. Licorice tea can help to quiet a nasty cough and a nice relaxing cup of Chamomile can lead you to a nice peaceful sleep. Adding honey or a squirt of lemon to any of these teas will also benefit the heath process. High caffeinated teas are not preferable due to the risk of a buzzing headache and adding milk might not be the best option for a phlegmy cold.
Of course any tea will help when your sick, whether it be physically or simply mentally. Just holding a warm mug can comfort you when you're feeling down. So if the medication isn't doing its job, take a second and brew yourself a cup. Happy Healing!