Periodontal Disease/ Root Canal Infection

On my visit to a specialist dental department of Guy's Hospital last Friday I was told I suffered from chronic periodontal disease and ongoing infection of root canal on my front upper teeth (the infection seems to have spread after having a surgery on one of the teeth 3 years ago).
In no uncertain terms the doctor then said that I MUST have the dreaded scraping and root planing, before they can do any work on trying to surgically get rid of the other problem, the root canal infection (which has already caused some bone loss in the jaw).
I told them I was being treated by my homoeopath, and taking Helios Tooth Mix remedy, but they said that there is no way anything can reach the infection, as the tissue around it is dead, and there is no blood flowing to it.
Are they right? Is there anything I can do?

SHORT CASE HISTORY

39 year old female, with a history of alcoholism - 5 and a half years in recovery, one day at the time. Always felt different, not quite fitting in, etc.

Smoker - petrified of giving up, feels like 'all will be lost' when even considering giving up.

Sugar addiction, sometimes tolerates it well, other times suffers from dreadful 'sugar hangovers'. Best when not eating sugar, but lack of self love, fear, or other people eating sugar makes her forget easily (taking one 1M Syphilinum/LacMat/SacOff powder every mid-cycle for the last 6 months, at night).

Not sexually active, misses sex and intimacy, but refuses promiscuity (looking for 'Soulmate':). History of codependent relationships, not an option any more, but hasn't yet learnt what else is available out there! Cautious.

Often feels disappointed, so keen on 'trying to release all expectations'.

Likes driving, petrified at driving on motorways.

Keen on using (daily) prayer, meditation,
Bach Flower remedies, reiki (level 2), homoeopathy, acupuncture and other 'alternative' and spiritual tools - no allopathic treatments in the last 4 years, except for dental.

Appearance very important. Well presented. Looks very confident.

Writer - frustration at not being published, so unable to earn the living from what she's good at.

Loves her children, but aware there's some fear involved (especially when spending time with them; feels like it's 'too much')

Trauma - lost home (very important) in the war (but was safe at the time), beloved father committed suicide; both happened about 15 years ago.

Last time felt completely whole and happy at the pre-nursery age (4), before 'joining the rest of the human race'.

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I hope this makes some sense, to someone out there... Thank you for reading!