Have to admit that change doesn't thrill me much either. Being prepared for the appointment with the psychiatrist may help ease the anxiety. After you have the made the appointment with the P'doc you can always phone where they work and ask how long the first appointment is likely to be.
Writing down issues that you deal with will help you to say all the things you need to say in the first session. The first point of contact is also an opportunity for you to ask questions that you may have. Again you are equals. It's not a parent/child relationship.
Your T should not be confronted by the fact of the appointment. If that is the case then that is their problem not yours. If/when you do make the appointment you don't even need to tell your T.
Wishing things go well for you.