For me, it's like maintaining connection with her, keeping me open and vulnerable, sharing my heart. I'm like a lonely child or lonely teenager or sometimes lonely adult wanting to tell her everything important to me.

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OP, as your therapist is OK with you emailing, email away. Trust that she will inform you of her boundaries and have a discussion with you if you're emailing "too much". She's a therapist and what better way to model stuff?