Thanks for asking the query,
After reading your clinical symptoms i would suggest you to go for the treatment of gingivitis
first followed by the extraction of the tooth.
I would suggest you to visit the Dentist
and get the complete mouth scaling
and polishing done.
As the prescribed antibiotics are not suiting you get it changed by the Dentist, after that you can plan for the extraction of the tooth.
Maintain a good oral hygiene
, take lukewarm saline and antiseptic mouthwash rinses.
Hope this helps out.