What Causes Skin Infection Around Nails?

hey, so i have the nasty habit of biting my nails, im trying to stop and im doing what i can to take care of them and clean them up, earlier i was using tweezers to pick off the dead skin around my fingers and when i did this to my index finger, an ooze came out of it, it looked almost like what comes from a zit only it smelled horrible, im just curious what that was...