Welcome to AA!
In answer to your question, once your tank has been properly medicated for the recommended amount of time, you can add fresh carbon to your tank which will remove the rest of the meds from the water. I would not add more fish until after the course of treatment. Do you still have the one cichlid in the tank? What size tank is it? IMO
you will not need to tear down the whole tank and start over but my concern would be keeping the cycle going with only one fish if the tank is large, the bioload may not be enough to keep things going. How long was the tank set up before the illness hit?