I think your relationship with her sounds lovely, and the only thing that seems wrong is "secret" aspect you mentioned above ^. She doesn't seem to be letting this be a dual relationship, which is a good thing. That may even be why she keeps you a "secret". She sees it as not allowing you into her personal life by knowing all these little things about her and being on a special list of people to call if something goes wrong. By doing all of this, she is keeping the relationship focused on you still even though you two ended your work together. This still seems very therapeutic. Her care for you appears genuine and all of these little gestures from her are the proof. She is probably just busy and has work and family to deal with right now, which is why you have not heard from her. She could also see it as giving you space and realizing you have a life and maybe feeling like you probably don't want to be bombarded by your ex-therapist constantly and you have bigger worries such as school, work, and your own personal life.
Even though there are reasonable sounding explanations for your concerns, it would be good to address the feelings in a conversation. Tell her you realize why she may be doing this, but that it doesn't feel right or good feeling like a secret. Maybe she will have an explanation or reassure you in some way? Just an idea. I hope everything works out!