how to treat a tooth infection don,t want a root canal or pulled?

Since you already have a crown on the tooth I would suggest getting the root canal in case it gets worse. If the nerve inside the tooth is inflammed and continues you could get a bad abscess that could also affect the adjoining teeth. Worse case the infection gets into your blood stream and causes other problems. You may be able to hold off but then again you might not. I would talk to the dentist and see if you could work out some kind of payment plan. I don't think they would have to remove the crown, just open it up, do the rc then apply a permanent filling.

If by infection you mean a hole in the tooth has reached the nerve and it is infected, then a root canal is the only option. If you mean the gums around the tooth are infected you can treat that yourself with the gargling method. Be aware that an infected root can cause an abscess and the abscess can cause a clot which can break off causing a stroke. A root canal is a simple procedure where the root is extracted and the canals in the tooth are filled. It is no big deal.

Your 3rd choice is to build a time machine, go back in time and take better care of your teeth and see a dentist before the tooth gets to the point where it needs a root canal or an extraction.

If the infection is because the tooth has died then extraction or root canal treatment are the only options. Antibiotics can't solve it and would be a poor treatment.

the only option for an infected tooth is root canal or extraction.

Tooth infections cannot be treated, they typically have to be pulled, or filled to prevent spread to other teeth/gums.

Very difficult to do and all the while you delay the infection becomes more established. There is a risk the infection might become well established and become such a problem it may well cause bone damage.

The risk is all yours.

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Gargle with warm salt water, several times a day

you might not have a choice if the tooth dies - you go to the dentist and have him look at it - if its treatable, you may prescribe antibiotics