I am a general dentist and I see plenty of children with abcessed teeth. It is really important for this infection to be treated because the health of the adult tooth may be jeopardized. Your dentist is the one who should determine treatment, not the hygienist. However, if you don't really fell comfortable with this dentist, seek a 2nd opinion. Extracting an abscessed baby tooth is a proper treatment most of the time; since the tooth was injured before, the nerve inside has died and is now infected. Just using antibiotics is not a solution, since the infection will come right back. As far as the pain, I have seen kids with huge swellings who feel no pain. Also, because the tooth is draining, the infection has an "exit" , therefore, there would not be any pain.
Never feel badly for questioning a doctor's recommendation; your comfort with the dentist is most important.
Hope this helps, best of luck,