a crescent shaped piece of index nail will not grow back, it just starts to grow up and detach from the nail bed just after the white crescent near cuticle. it would just grow up and bulb out there, so i trim it down. i notice very short, very thin black "hairs" around the area in the nail bed.

ANY CHANGE in the nail plate is cause for concern and from the sound of yours, I think I would see either my doctor or my dermatologist NOW!