What is the treatment for dental infection?

Hello doctor,

I have a bad infection at the lower right molars- 46 and 47(and another one at the left one, but that does not hurt and I will deal with it right after this one). I had really big swelling and a lot of pain, swelling started a few days ago and got gradually worse. I went to the dentist and he suggested an extraction for both right molars, he said I have a cyst and an infection, that the previous root canal was cemented, and that redoing it would not save the teeth. Gave me an antibiotic (Amoxicillin and Clavulanic acid every 12 hours) and something for the pain. It is been three days now since I was supposed to have my two molars removed, but I canceled the extraction(the dentist also told me I was still a bit too swollen to do it today anyway) after I got a second opinion from another dentist. As I am only 24 years old, she(the second dentist) does not want me to remove either of them, telling me to try and redo the root canal on 47 and 46 she recommended drilling into the bone to drain the cyst and save the tooth but recommended another dentist with more experience to do it.(Who is completely booked and cannot take me) so I found another dentist. When I went to the original dentist to cancel, he told me what I had was very serious, that the teeth could not be saved, and that I had developed dental cellulitis. Now I am scheduled to the third dentist, in two days who has seen the x-ray and told me to not have them extracted just yet but instead, to continue the antibiotic until Friday and we'll see then. The swelling has reduced but is still present a little, and the pain is mostly gone, with no painkillers taken, but my cheek has a hard spot, and I feel a little tension in that spot whenever I move my head up. Apologies for the long post. Is there any chance that the teeth can be saved? Or should I hurry and get them extracted as soon as possible? The contradictory opinions from these three different dentists have me worried. I read online that a dental cyst can lead to the removal of part of the jaw. So I do not know what to do. Kindly suggest.