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Thank you for your question and welcome to Just Answer.
The antibiotic we usually prescribe for tooth infections is Amoxicillin or Penicillin. If you happen to be allergic to these the second choice is Erythromycin.
However, keep in mind that antibiotics alone will not cure you of your infection. They will reduce it somewhat, but once you stop taking them, the infection will return. This is because the source of your infection, the tooth, needs to be treated and that involves seeing a dentist. Using pain medication and antibiotics just treat the symptoms of your problem, the pain and swelling. An analogy would be taking pain medication for a thorn in your foot. The medication makes you feel all right but when you stop the pain medication, the pain returns. You have to treat the source of the problem (removing the thorn), to get better. I hope this answers your question.
If you have any concerns regarding this issue that I have not addressed, please let me know and I will get back to you with more information.
Sincerely, XXXXX XXXXX DDS
Yes, if it is an upper tooth. An infection on the nerve of an upper tooth will come out the tip of the tooth which is near the sinuses. If you have large sinuses, the infection could very well infect them as well. I hope this helps.