First thing first A stitch in time saves 9. What the lil is going through is probably due to delayed dental care or missed follow up visits.
Plz understand the tooth is a closed compartment, with the infection finding a way out through the path of least resistance that is gums. Hence the swelling, The swelling usually increases in size and establishes drainage. In the event of non establishment of drainage, the swelling may increase in size causing fever pain. Only then does it warrant an antibiotic coverage.
With the current pandemic and least traumatic dental experience would be to extract the tooth followed by a space maintainer. To know more you may peruse through the space maintainer section of our website, Vanilla Smiles pune
https://vanillasmiles.dental/services/space-maintainers/
stay safe stay indoors
Next Steps
If pain fever persists plz start a course of antibiotics
Health Tips
Avoid root canal procedure since the prognosis is already compromised due formation of pus.