I think what you're describing is a private practice set up where somebody else handles the scheduling and probably the billing other than the therapist(s). It's the model for most private practices in the U.S. In that case, she may not know that you couldn't make an appointment for next week, but I am not sure there's a whole lot of purpose in saying that, unless you want to be put on the cancellation list, if there's such a thing (there is in my t's office set up).

Otherwise, I'm not sure that I would engage emailing given your described attachment issues. Are you prepared to deal with the fact that she may not reply or her reply may be not what you expected and/or wanted? Seems to me this happens pretty often. Perhaps it would be better to have a conversation directly with her about the topics of your proposed email. Sometimes I think bringing email into the therapy relationship messes with the intimacy of what happens in session. Like with new love, there is such a thing as too much process and discussion, and not enough doing/being present in the relationship itself. Which happens in session. I think your feelings are really great and I get the urge to share them with her via email, but I think a little restraint might be good here, to sit with them until you see her again. Talking about what you experienced in the first session would be a great opening to the next one. It preserves the continuity between sessions and allows you to relate to her, to have an interaction around it, rather than a static talk-at experience.