RCT or EXT? Whether or not to do RCT or extract the tooth depends upon many factors. Unfortunately that is not something we can evaluate over the internet without actually seeing the tooth and an x-ray. If the infection is too large, if there is not enough sound tooth structure or if the tooth has severe bone loss, you will loose the tooth anyway even if RCT done. Trust your dentist or get a 2nd opinion.
Dental abscess. See general information below: http://www.webmd.com/oral-health/guide/abscessed-tooth#1 The specifics of what is required depends on the extent of the infection. Recommend seeking advice from a dentist licensed in your area for specifics for your situation.
Gum Boil. Indicates infected (abscessed) tooth. Pus leaking through bone under the gums, causing gums to swell. Most effective treatments are root canal/crown or extraction/implant/Crown. Incision & drainage and/or antibiotic therapy may be required. Course of treatment is made by your Dentist after evaluation of the extent of the infection and the amount of damage to the tooth and surrounding tissues.
More info needed. A dental abscess can be caused by a number of different conditions, some treatable, some not. Your dentist apparently feels the tooth is hopeless. If you feel a second opinion from another local dentist who can examine you is necessary, please get one.