I am a big boundary person both for myself and others. ( I didnt learn them until I got sober). I set them for myself and try to respect them for others. Since you didnt ask I would personally wait until next session. If its dire I would first email asking a- if its alright to email, b- if this email is personal or private and c- if its not personal or private is their one that the therapist would consider using?
I would do that rather than dump it all out without checking first.