I had a load of dental problems when I was younger, and I'm the eldest, my sister's teeth are just as bad really!
I was basically hooked on dummies, and it preventing my teeth from breaking through because I constantly had one in my mouth, so by the time they did come through, I had a full grown adult toother pushing through the roof of my mouth behind both my 2 top front teeth!
in total I had about 5 or 6 extractions along with about 4 or 5 fillings (I loved sugar, what can I say?) but I was never put to sleep for it
I didn't like the needles though, whenever one entered my mouth I would constantly lash out at the dentist! So I kept getting refurred to all these different dentists...
where I eventually was seen to by this one dentist who not only gave me happy gas! but also went out of her way to study hypnosis so it'd calm me down enough to go through with everything, and it worked!
looking at my teeth now you wouldn't think I had to have braces for a year and several years of toothache!
Though personally I would get another dentist's opinion, to go out to sleep at such a young age just for some extractions is ridiculous and it'll cost a bomb surely!
I don't think doing it all in one go is the best option either, I ached all over after having 1 blinking extraction...never mind having 6
I'd be in agony for a week with that personally!!!!
See someone else, and remind me not to see your current dentist