Suggest Treatments For A Deep Cut On My Finger

I cut my finger with a circular saw a week ago on my left hand forefinger at the right side below the nail. A lump of tissue was ripped out but still attached to the skin as a letter box effect. i pushed the tissue back in the hole and bandaged it and it has since scabbed over but feels almost hollow underneath when the scab is tapped. It is now feeling bruised around the scabb and is very tender. Have I done the right thing or should I have removed the tissue?