I went ahead and took out all the frayed wires out of my bathroom. There are no wires, receptacles, or switches in the bathroom.
I also removed the old j-box and installed a new steel one. I put the feeder wire in the box, secured the bx with a clamp, then secured the ends with a wire nut and e.tape (all individually). There is also another bx cable in there that is supplying power to a hall light and two receptacles. I didn't connect it the feeder because I can't tell which wire is hot and which is neutral because both wires are sheathed in cloth. Every wire has a wire nut and tape around it individually inside the j-box with a cover.
Am I good until I can call an electrician in the morning? I've had it, this stuff is making me a nervous wreck.