CBT certainly does address this issue too

In fact, you're probably using CBT if and when you do discuss this, as it's something that is happening right now, in your thinking and causing you to behave a certain way. It's important to discuss it eventually, so that your behavior is appropriate and not causing you to feel ashamed either.
There are some Ts who are afraid of the attachment unfortunately, IMNSHO. At least they act that way, very stand offish if a patient mentions something in the way of attachment. I'd bolt for the door if any T blocked my energy that way.
It is good that you care about and for your T. Make sure that the caring doesn't go into worry, as that isn't good. (For others out there reading...) A T can take care of her/himself, and should. Don't worry about what you share or what you are going through affecting the T too much or causing her/him problems. Ts have their own ways of talking out there sticking points, usually with colleagues
Good wishes to all!
Maybe we should ask DocJohn to add a shirt with something like,"promote world peace, love your therapist" or something