Got a doozy.
Hmmmm, I believe I know one sociopath and what made it apparent was his lack of interest in other's well beings. For example, he was telling a story of somebody driving his car (he was passenger) and how this guy hit a pedestrian. Now my H and I kept wanting to know if this person was alright, but to him she was a minor part of the story - the bigger story was the dent in his car. It took us several attempts to finally hear she was alright. Since that story I started to see him differently and realize his characteristics are odd.
I would GUESS if unless she is not capable of being empathetic, it's not a sociopath (a.k.a. antisocial personality disorder).
I suffer from anxiety/panic. What you first explained sounded a lot like anxiety disorder - but then you stated she shaved her head & did her make up like she is sick.... Now maybe
She may not be lying on purpose. She may be a hypochondriac. There doesn't have to be a lot of drama around it. The girl can say "I have terminal brain cancer." The response can be "So sorry to hear that. I hope you can enjoy the time you have left."