Do symptoms from a blood transfusion and complications go away quickly?

It depends. Some complications from blood transfusions may persist for life, like an alloantibody against red blood cell antigens, specially anti-d. Others like hemolysis or fevers may solve in hours after stopping the transfusion.
Usually. Most symptoms from a blood transfusion such as fever, chills or itching are limited and resolve quickly. More information about the complication would be required to answer more completely.