Can they put me out to fill a cavity?

Last night I went to my dentist for two fillings. He gave me two rounds of shots and I still felt him drilling the tooth. We were not able to get half way through the first tooth and called it a night. I don't know why as I get older I have a hard time getting dental work done. I get so worked up that it makes the novocaine wear off quickly. He wants me to take xanax, gas and the novocaine shots but I would prefer just to be put out. Do any dentist do this for two cavities?