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While it is not really anything that is really common, it certainly is something that can and does happen. In particular, with the tooth being a rear tooth.
I'd try to get to your Dentist which you prefer as soon as possible, take pain meds, if needed, and you may be in need of an antibiotic - just another reason to see your Dentist to get the antibiotic.
So summarizing: I'd get to your Dentist of choice pretty quick, so the swelling and or other problems can be addressed, and before your symptoms and or others get 'potentially' worse.
I hope this helps you. Please let me know if you have any other concerns - OK?
Amoxicillin is a good one to do what you want. It is meant to take care of the swelling, yes.
I'd keep taking it. Likely it will reduce the swelling. But, 'do' keep in touch with your Dentist should things go 'south'. Hopefully though that will NOT happen.
Sorry, last night I went to bed.
How is the swelling? Any better yet at all?
*Please let me know how I might be able to assist you more please - OK?