transference is one of those words that are used in many ways given the situation, location and therapy approach.

heres a link that explains some of the ways the word is used in the context of mental health.

http://medical-dictionary.thefreedic...ce+(psychology)

here our therapists use the all but the 4th one when discussing transference.

here we use the words "attraction" and "attachment" for when a client develops strong caring for the therapist type emotions of which you describe in your post.

talk with your treatment provider they can explain what the term is that is used with that therapy agency and where you are located. you dont even have to tell them its you. you can say you read somewhere on line that some people feel this way about their treatment providers and you were wondering if theres a term / word for it.