something you said about the transference struck me... you mentioned growing up feeling ignored. I would say that is being activated with this lack of immediate response from T. Chances are, she missed the email or has not had a chance to respond. As someone else stated, there's no therapeutic value to her "not engaging" in this email exchange, since it's a logistical matter.
Can you either try her again (perhaps leave a message instead of email), or wait some more for a response?
I would also bring this up with T at the next appointment...