As someone who has just been thru a major rupture with my own therapist thru boundary issues, i would suggest if rejection is an issue for you that you ask her to clarify boundaries rather than waiting until you accidentally bump against one. Boundaries can be things like policies on time, on outside contact ie email and text, is she available for emergency/crisis contact, what is a reasonable reason for calling etc.

Also i would make sure she is equipped to deal with your issues. Because you don't want to invest your time and your heart with someone who is going to get half way thru and decide she's not the right type of T for your needs (also happened to me! )

Also feeling attached to your T is perfectly normal, you'll see many people on this board are attached to there T's. But i understand it is a scary thing

Welcome to the boards x