foul smelling spot on my gums

There was a tooth that gradually decayed and fell apart and out leaving just the root inside which you can see is brown peaking out the middle and it smells foul! I cant afford a dentist and it really disgusts me but doesnt hurt so Ive tried everything to make the smell go away. Ive tried digging out the peices I can see protruding with a needle. Wiping and wiping with alchohol swabs and the more you press the more the odour is released it seems! Ive tried inserting the needle tip to try and suck out would be infection goo but to no avail. There doesnt seem to be much in there besides the grossest smell ever!
And weirdly everyonce in a while I guess the infection must find an outlet an eventually forms a white bulb over top the area just on the side of the gums which when pressed lightly snaps open easily and hard white pus goes flying out painlessly which does not smell at all!! Weird. What the hell do I do here? Can I dig it out and eventually pull the rest out?
Its driving me nuts! The wreeking stink!! No matter how much I brush or soak it in alchohol the smell doesnt even dissapate. Not even a little. I could soak and wipe with alchohol for an hour and its the same old strong rot smell.
What do I do????????/ Help?????? Icky yuck yuck!