Hello, I am sorry to hear of your sore gums and troubles...
Red and often somewhat puffy gums, located in the back corners of your mouth are, as you would expect, quite likely associated with 3rd molars (wisdom teeth). Generally wisdoms don't erupt till one is about 18 years of age or older. My suggestions on a Sunday night late:
1) Take the pain reliever you've had the best luck with previously, such as Advil (Ibuprofen), you could take 600 or even 800 mg every 8 hours. Alternatively, you could take Tylenol, if it works better for you, you could take up to 1000mg every 8 hours. These are high strengths and adult strengths for one who is 18 years or older. Take one or the other , but NOT both medications at once.
2) I'd try to get to the Dentist of your choice tomorrow, asap. Because, while this sounds like wisdoms wanting to erupt, and even though the pain may come & go, it will inevitably return again and often with additional intensity of pain. So, please do get to your Dentist asap, tomorrow morning if possible.
3) If it is wisdoms and it likely is, don't let it worry you... I'm fully aware of all of the horror stories out there. A couple of such stories here & there are actually even true. But 98% of the time wisdoms are NOT difficult for you the patient or recipient of the extraction/s.
4) Try to get some sleep tonight!
I hope this helps you, at least some. Dr. Rampton
*PS: I saw the question earmarked for another Dental Expert to answer. He is likely in bed, as he lives in an eastern time zone, and it would be nearly 1 in the morning there. So I answered your question. Good night! And, hang tough. Your pain & Dental trouble is totally fixable. Just see your Dentist asap - OK? Best wishes...