Yikes. When your T talked about "professional" and "boundaries," I think she was talking to yourself, not you. She clearly has a different sort of relationship with (or feelings for) you than is typical for her with clients, and it's making her uncomfortable and insecure. She definitely needs supervision, and perhaps her own therapist to help sort this out. It's not on you.

I am a T-in-training and my T and I have as a therapeutic goal to shift the relationship from client-therapists to collegial over time. This is a necessary goal, because our community is small enough that we already have overlapping relationships, we know many people in common, and we will run into each other in professional settings. So it's not wrong, per se, to have a therapeutic relationship that is atypical because of your shared profession, but this needs to be done carefully, thoughtfully, intentionally, and with transparency. And without your T bursting into tears.