Thanks for sharing your concern.
Swelling,pus,pain are features of infection.so you have developed infection behind your two bottom teeth.
when you push on it the white stuff which comes out is pus.(which has numerous bacteria,their debris and bacterial products).It is infective.
you history says that you maintain good oral hygiene
by brushing,flossing and using mouthwash.That is really nice,but these measure that you are following comes under maintainence therapy.
If already there is some infection established,then that should be cured first after that definitely maintainence of hygiene will help you lot.
Therefore i would suggest to visit your dentist
for clinical evaluation and as there has been deep pocket developed ,it should be treated by deep pocket curettage and root planing procedures.
Maintainence of good oral hygiene will keep your oral cavity healthy.
Hope i have answered your query.