Hey, I Have A Bad Tooth That I Never Got

Hey, I have a bad tooth that I never got removed and it's basically gone already by itself and now there is a tiy little piece of tooth fragment clinging to the side of my gum. I an move it around alot with my tongue and it doesnt hurt but i tried to take it out nd it wont come free and there is pressure when i try to yank it a bit with a little tweezer. How can i make it come loose instead of setting up an appointment with a dentist. I don't have insurance so I would have to pay cash and I can't afford it