First of all, I don't think an email delay of a day is a big deal. Many people do not respond to email right away.
I am, however, saddened for you when I read of your general trust issues, even with a therapist. Working with a therapist isn't at all about "breaking you." It's much more about discovering wounds and healing in order to enjoy a more fulfilling life. Therapy is a good "testing ground" for starting to trust.
I hope, some day, you can allow yourself to open up enough work on this.
Although it can be scary, I do think you'll have an opportunity for a much more fulfilling life.
Best wishes for your move and your new job!

WC