Can i go under general anaesthetic, or don't i have a choice?

I had an infected tooth, so they gave me a temporary filling and sent me on my way for a month before returning to have it removed. My dentist was ill the day i was meant to have my appointment and as im petrified of dentists i didn't ring in to re-arrange....my fault i know =( gradually my tooth as broken apart and all i am left with is what is under the gums. My new dentist said will have to cut my gum to remove the rest of the tooth can i ask for them to use a general rather then a local anaesthetic? I would rather get advice from others before asking my dentist as i don't want to come across as totally stupid for asking x