From the picture you are showing, there seems to be wisdom tooth which unfortunately is angulated and doesn't have enough space to erupt in your jaw. It causes immense discomfort, pain , swelling in and around the gums.
Next Steps
Consult an oral surgeon immediately as this needs to be removed surgically. The procedure is quite common and is usually done in an outpatient clinic set up.
Health Tips
Till you get yourself checked by the surgeon, you can do some warm salt water/betadine rinses/gargles 3 to 4 times a day. Any anti inflammatory analgesic( pain killer) medication should help.