Thank you for your question and welcome to Just Answer.
If you can't have the root canal done, you need to have the tooth extracted. The problem is the dead nerve in your tooth. This is the source of the infection. Antibiotics and pain medication just mask the symptoms of the problem and only help as long as you are taking them and do nothing to eliminate the source of the problem. Until the source of the problem, the infected nerve of the tooth is removed, either by doing a root canal or removing the tooth. you will not have any permanent relief of the symptoms. Yes you have an infection but you are far from having to worry about the infection spreading since you are still taking antibiotics. You will not get a brain abscess, but left untreated the swelling can get quite large, extending to your face and into the deep spaces of your head and neck. Most people will not tolerate the infection getting to this point and have to have the tooth removed much before this stage. This is not serious, yet. My advice is to have the tooth removed.
I hope this answers your question. If you would like to discuss this further or have any additional questions, please reply to my answer and I will get right back to you.
Sincerely, XXXXX XXXXX DDS
If Advil is not helping, then you can try this trick.
A very good way to control dental pain using over the counter medications is to switch between taking 400 milligrams of ibuprofen (e.g., 2 tablets of Advil), and 1000 milligrams of acetaminophen (e.g., 2 tablets of extra-strength Tylenol) every 3 hours. Be careful not to use these medications if you have had previous adverse reactions to either, or if you have had gastritis or peptic ulcer disease in the past, or if you have liver disease. Anything stronger and you will need a prescription which will necessitate you talking to your dentist, physician or a visit to the ER.
In addition, you can try "Toothache Drops" available at your pharmacy. This is clove oil (eugenol) which is very soothing to an exposed tooth. Place a drop or two on a cotton pellet and place on the tooth or on the hole of the tooth.
If you cannot afford a root canal, you cannot afford a root canal. Your dentist has no other choice in treatment than to remove the tooth, otherwise he is abandoning you as a patient, something he is not allowed to do. Call another dentist and if they are hesitant to remove the tooth, tell them that you are coming to him for professional care and to be treated and financially you can not afford the ideal treatment. He is obliged to offer you the alternative treatment and if he is not comfortable taking you tooth out, should refer you to an oral surgeon who will. I hope this helps.