K.A.
Yes a root canal can be done on baby teeth and in young children. They are called baby root canals or a Pulpotomy and aren't the same as an adult root canal. It's actually better to try and save the tooth this way then have it removed.
You should see a pediatric dentist and they will explain it and take care of it.
If her mouth is swollen it means there is infection so she needs to be on antibiotics asap. An infected tooth is nothing to mess around with or let go!