My name is Martin Kostir and reading through your posts, I though I would leave a comment as I am AT teacher myself.
First of all, I don't have any form of anxiety (I started with AT to help my chronic back pain), however I did / still do work with people with all sorts of anxiety.
The interesting thing is that quite a number of my students would start having lessons with me to improve posture / relieve pain, but only after some time, when they build a relationship of trust with me as a teacher, only then they would bring out the fact that they suffer some sort of anxiety.
The nature of the technique invariably leads to this revelation.
Few points to mention about the main principles of AT.
1/ It deals with body and mind together - so no matter why students start having lessons, they end up improving both (so yes, it does have positive effects on your mental state).
2/By it's definition, AT is a skill that teaches you something new that you don't possess as you start. This new experience is different for every student, even for each individual student in different lessons. You always learn something new - that's the nature of the work.
3/Yes, generally AT lessons seem to be expensive at first. However taking in account how effective it is, it may end up being the cheapest solution to a problem.
Example: Most of my students have chronic neck / back pain - that's my specialty. When they come and I tell them that they might need 3 - 6 months worth of lessons (600 - 1400 AUD) they just role eyes inside their eyes.
Then we do the maths - and it ends up that in the past year, they would spend 6 thousand on chiropractors / drugs / physios. And suddenly, it doesn't seem to be so much. So yes, it is relative.
4/ Can you learn it yourself from a book?
Well, Yes and No.
F.M.Alexander figured it out himself. He had no teacher, he was the first.
So yes, it is possible, but you have to take in account the context.
He spent years of his life dedicated to his investigation. Hours a day in front of a Mirror observing himself. He came from relatively wealthy family, so he could afford doing that.
So if you don't have his commitment / passion / dedication, you will NOT learn it on your own. No way.
The teacher is a extreme shortcut (yes, I know it doesn't look like it at first) , money and time saver. Do yourself a favor and see a teacher if you want to explore more.
As someone who already was through the training and who teaches it now: AT will teach you something that you don't have any idea about until you learn it. The only way to understand it is in retrospect.
I give an analogy of the movie Matrix. Neo had no idea about matrix until he was unplugged. Now get into Neo's skin at the start of the movie. If someone would try to explain to him what the matrix is inside of the matrix, he would not understand / believe. Everything became obvious only after he took the step aside and got a new perspective.
Alexander Technique is very much like that.
Hope this will help to some.