I would recommend getting a second opinion from a different pediatric dentist, and ask in advance if they do in-office conscious sedation. That is sort of an in-between step, not as extreme as GA, and is a pretty common practice, from what I know.
It sounds like the tooth has abscessed, and that's why the dentist recommended extraction? I have some experience with this, sadly. If the tooth has a deep cavity, and there is enough structure there, they may do the pulpotomy and place a crown, and hope that the tooth can survive to shed naturally. If the tooth gets infected though, called an abscess, it's really unlikely to heal and can infect the bones of the face, be pretty serious, etc. They might try antibiotics before pulling, but the prognosis is not good to save the tooth.
You can PM me if you like. There is also a Yahoo group called "veryyoungkidsteeth" that has lots of info about dental procedures for really young kids. Several dentists answer questions there. Good luck.