It has happened to me - even though the circumstances are different. Once I read to my ex T something I had written about my grandmother, whom I’m really fond of. Then I looked at her and she had tears down her face.. She then explained that her own beloved grandmother had just passed away, and she was touched in a positive way by my letter. Long story short, we talked, she assured it was ok, I was comfortable again. Also, we were at the end of therapy plus I’m very easy going about Ts being human and she had disclosed something about her personal life with time (for therapy purpose).
Anyway, I find that these Ts have empathy, which may feel weird to us but is a sign of kindness and being truly invested in your client, at least imo. From what you said, she was really listening and feeling you. Connected and willing to see you feel better.
Talk to her again about it if needed, one day it will be easier.