It sounds like she has some issues of her own she needs to work through and it is not right of her to project those onto you and this situation. It isn't fair.
I'm sorry it feels so crummy.

I can understand her to some extent though. My T had never told me she cares about me it has always been a generalized "so many people care about you".
She had always showed that she cares. So many caring words and gestures that I know make her a unique T from what I've experienced and reading about the experiences of others.
I think everyone, T or not, has their own "language of caring". Some are more verbal, some aren't, and some use gestures and words simultaneously. Words can be uncomfortable for some people. They're too vulnerable.
And unfortunately there are even those Ts they will verbally say they care about you, but will never show it through gestures and prove the validity of their claims.
-Hope