All perfect praise be to Allah, The Lord of the Worlds. I testify that none is worthy of worship except Allah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and messenger.
Use of anesthetic injections for dental treatment during fasting is permissible, because anesthesia is neither food, nor drink, nor something to their effect. Moreover, nothing of it reaches the throat. When one is receiving dental treatment during daytime in Ramadan, he has to be cautious to not let anything reach his throat.
Allah Knows best.