Quite often a gum infection can be treated just by rinsing the mouth with very warm(as hot as you can comfortably tolerate) salt water(perhaps a teaspoon or two of salt in a cup of water) several times a day. I have had a few gum infections I treated this way. If the warm salt water doesn't work, then you can alternate rinsing your mouth with hydrogen peroxide and salt water. Just be very careful not to swallow the peroxide.

Do you use a waterpick? Pehaps there might be food caught in the gums there. Sometimes there is a small bit of food so deeply lodged that flossing and brushing won't remove it, but a waterpick might remove it. Have you had a dental cleaning recently?