Sounds like your T. didn't know your DBT's boundaries. I am not supposed to text my T. unless it's for appointments and she doesn't email or call. So, if I need extra support I am to ask for another session.
You are not too much for DBT fascilitator - they just have different boundaries than your T. And, your primary sounds busy but did try to offer an alternative solution.
They aren't rejecting you and it's not personal. You've had really relaxed boundaries with your T. and not everyone will have those same relaxed boundaries. Just like I would have different boundaries than you would when interacting with other people.