The uncomfortable feeling probably stems from you exposing deep feelings. And coming from the client's side it feels more vulnerable because of the inherent power dynamic of this relationship.

I hear that you don't want to bring it up but a 'good' T would bring it up themselves i.e. what it means to you and (hopefully in the case of your T because she said it too) what it means for her and where you both go from there. I think this distinction is important to make and probably why some (professional / ethical) Ts discuss it with clients and are wary of using this term.

I am not implying that your T is not ethical or a 'good' T as she has shown that she is not a 'typical' T. But yeah, it is a loaded word and can carry a lot of expectations or mis-alignments, mis-direction, mis-interpretation... so I think that Ts ought to be careful when 'love' is in the room.