It seems like therapists have very different ideas about what out of session contact is healthy and ok. So I'm not sure that there is a baseline. You didn't do anything wrong. You asked her if you could email her and she said "yes." If she only wanted you to email to schedule or to get in contact with her if you were in a crisis she should have told you then. I can understand you feeling badly about her response, but you didn't do anything wrong.

With one of my therapists I have no out of session contact. I don't have an email or a cell phone number for him. If I need him between sessions I would have to call his office line during business hours. I'd have to be in a real crisis to do that, and so far I haven't been.

My other therapist does allow email. She always responds, but her responses are pretty short. I think that she just prefers to talk things over with me on the phone or in person. I have emailed her when I'm having a major problem/but not an actual crisis and she has given me an extra session. I actually regularly email her before every session...pretty much with an agenda of what I want to talk to her about.

I'm not sure that any set of therapeutic boundaries is necessarily right or wrong, but I do think that the therapist needs to be clear about them and they need to be consistent. I'd definitely bring it up to her in your next session. I think she was unclear about what was OK, and she needs to know that caused you some hurt. In the end I bet you can work it out with her, but she needs to know how you are feeling.