It's possible to have them out there. The problem is finding the proof. The track of a mountain lion is like any other cat track except size. Unfortunately unless there is a reference in the pic you have, it is inpossible to tell exactly what size the track in the picture was. Could be a mountain lion, or a bobcat, or a big house cat. As for the screaming sound , it could be. However like was mentioned Bobcats sound like that as well. Also you get a cub black bear hollering for mom they sound like it to, however wrong time of year right now.
I've heard we have them in my area of NC as well. The western part of the state I could totally see them being there. However I haven't seen the proof that I need yet. As for around my house, I'm not sure. Of course a few years back I found a dead bobcat and I didn't think they were around in any big way so what do I know.
It's kind of funny this topic came up. Two nights ago my wife ( a police officer) got a call about a "cougar" sighting. She sent my the call report and the witness spends time out west hunting cougars and other big game as a guide with cabelas. So, who knows but officially No there are NO cougars in NC.