Hello madam,            Hope you are doing good. Nothing wrong in giving anaesthesia during 2nd sitting.Generally root canals are done to clean the infection inside the teeth. During the first sitting the anaesthesia is given to anaesthetize the pulp inside the tooth and the periapical area (area beyond the tooth) by which one cannot feel pain. After cleaning the infection and completely removing the infected pulp the infection regresses slowly within a week. The time gap matters depending upon the infection.When the infection completely regresses, by the 2nd sitting you will not feel pain. If the infection persists the pain may be present and by the time using anaesthesia is not a problem and it will not cause any side effects. And anaesthesia will be given only if needed in the 2nd sitting depending upon the healing.It will be known to the doctor by x rays or by opening the tooth for 2nd sitting.

Dear sir/maam, it's not mandatory to give anesthesia every sitting, completely depends upon the tooth health conditions. In your situation if the teeth having any extra canals or  curved roots,,, the pulpal reminents will remain over the canal.... At the time of 2 nd sitting you may experience pain.... If pain is simple might not get anesthesia... Severe may give anesthesia for better irrigation of canals... In root canal procedure.