I think it would be up to your therapist to set these boundaries.

I would like to encourage you to talk about your emailing with her and discuss why you feel you need it and ask her about her boundaries about out of session contact.

If you feel she is a bit frustrated with your emailing, then it's best to go in with a non-confrontational approach, like saying why it is beneficial for you to email but explain you want to respect her boundaries and were curious what her thoughts are about it.