"However, I never noticed any lack of empathy in myself. I haven't really worked out if that is because I just don't understand it, or because I really do have empathy. I know that I can watch a sad movie and be so into it, that I feel sorry for the characters and start crying in appropriately sad scenes." quote shakespheare

If you are moved in a "sad" movie and feel for the charectors, you have empathy IMHO.

My mother was not loved and cuddled as a child growing up but she definitely is empathetic and was a loving "caring" mother. She was very vain and loved attention, probably had a bit of "narcissistic" traits to her, but honestly, a lot of people have "some" narcissitic traits to them. My mother's love was always "unconditional", it was not all about "pleasing her".

Idk, I think your T is mistaking "PTSD apathy" for NPD. Is your T a PTSD therapy provider?