Child, 6 years old, has 3 cavities.

Why is GA your only option? Fillings are unpleasant but not traumatic, and you might find his attention to his teeth improves! The only child i know of who needs GA for fillings is my severely autistic cousin who melts down when people touch him :/

Also, is he brushing his own teeth? 6 is too young for that, i think up til 7 or 8 they don't have the required dexterity.

Talk to your dentist about your options. My daughter had a filling and the very sympathetic dentist made it very tolerable for her. She didn't even seem to feel the injection to numb her gums. I wouldn't go down the GA route it's not necessary. Ask them how they deal with children's fillings and get them to talk you through it.

Oh bless you op.
I worked closely with a few paediatric dentists when I was wondering whether to specialise or not. In my experience they are fantastic with the children and parents plus they've seen it all before so please try not to worry what sort of reception you'll get etc. They'll go above and beyond to make sure your son is comfortable.
I'm assuming the teeth weren't in too bad condition otherwise they might of suggested just removing the baby teeth. Obviously a filling age 6 is young but it's not the end of the world, and you can change things to ensure this doesn't happen again.
Going forward you say that he brushes his teeth, is that on his own? At age 6 they're too young to do it properly so if you can you or another adult needs to do it/ allow him to practice then you go again over them. If teeth brushing is good and effective a little sugar in his diet will be okay.