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I can understand this pain. It is like erupting pressure pain caused at every 2 to 3 months interval. Since you are done with Advil (Ibuprofen) and it is not going away. Please start taking the following antibiotic regime as soon as possible. Tablet Augmentin (Amoxicillin) 625 mg twice a day, tablet Metronidazole 400 mg twice a day, tablet Brufen 400 mg three times a day. Do a course of all these medicines for 5 to 7 days. An infection will subside through it and hopefully, you will be at peace for a month. You can repeat this course every two months if condition recurs. If the pain does not subside through this course then sure go to an emergency room.
Moreover, do salt water mouth rinses. Take a 1/4th teaspoon of salt in a cup of lukewarm water and do its rinses three times a day. Take mustard oil put a pinch of salt in it, make a paste and apply on swollen areas inside the mouth, at gum line before sleeping. This also helps in reducing swelling. Give me a followup after three days. Stay happy and blessed. Indeed, there comes ease after every difficulty or pain. Take care.