You need to wait atleast 24 hours after the extractions. That way the area has time for the blood to clot and you will not have a dry socket which can be very painful.
The local anesthesia commonly used in dentistry is a lidocaine 2% with a 1:100,000 epinephrine. this anesthesia will wear of within 1 1/2 to 2 hours after it is given. There are however some more...