You should definitely bring it up at your next appointment.

A couple of weeks ago, my therapist brought up the same thing. For her, it was about how she handles the texts. Sometimes she reads the texts and is left holding my "stuff" and it appears I often tell her and let it go. She made sure to tell me it was about her and she wasn't saying I couldn’t ever text her but it should be reserved for emergency situations and scheduling. Nor did she want me to think I had to take care of her. I instantly shut down so really did not speak.

I was shut doen the next 3 appointments (I currently see her twice a week)I was hurt. I then brought it up again. First we explored how ut made me feel like she was pusing me away and saying I was too needy and how this goes back to my core issue of abandonment.
We discussed the benefits of me texting her. How I feel after texting her, what are some other options (writing it down and texting her right before my session, journaling etc.). She talked about how she occasionally reads the text and emotionally holds onto it because she can't process it without me. It was not discussed but I think it happens mostly when my message has been about what something that happened in an appointment and her think I was blaming her for how something was handled.

In the end we agreed that I can text her but instead of putting what I needed from her at the end of the text, I will put it at the beginning. If I am venting because I am overwhelmed, I will say so. If it is a topic that we need to discuss at the next appointment I will say so and she will refrain from reading until just before the next session. If I need a response, likely a call, she will read it and respond. She knows how texting is an important part of my therapy and it always has been with both her and my long term therapist. This plan allows for both that and for her to maintain some boundaries.

She knew it would be a difficult conversation but we both agreed it was important. I reminded her that in the beginning she told me she would telle if texting became an issue.