Just for 24 hours, you are ok to drink Chinese tea. Please make sure that you don't continue further with teas, etc. and water fasting.
To clear up your eczema you should clean your liver. When liver function is compromised your skin does part of liver's job. Go to Liver Flush Forum and learn about liver flush.
Also find out what foods do not agree with you. If you are consuming processed foods and sugar, then that has to be eliminated from your diet.