You didnt mention upper or lower jaw. If upper then do you have a recent history of cold or infection ?
For now it looks like a possibly decayed tooth that has got active infection spreading around the anatomical spaces inside oral cavity as per your history . Do you have any accompanying fever or bad breath too ? Would be pointing towards infectious processes inside the mouth .
It could also be some food lodgement in that area causing inflammation on a second thought.
To combat pain, you can take ibuprofen tablet (combiflam tablet available otc) but please avoid it in case you are asthmatic, have any blood disorder or recent drop of platelet due to any condition, hyperacidity or gastric/peptic ulcer history or any other medical condition that contradicts use of this drug. And yes do not take on empty stomach. Add an anti acidity tablet as well.
Please do not take swelling lightly and show to a dental clinic nearby.
First step would require a thorough oral examination and accompanying radiographs as your doctor suggests. Go by the antibiotic regime if your examining doctor prescribes you. The treatment plan would be decided as per final diagnosis of your condition.
Best of luck.
take the painkiller as mentioned above and visit a dentist at the earliest as swelling may proceed further to other areas of face too.
avoid self diagnosis and treatment and avoid ignoring the condition right away.