Many musicians, actors, dancers and athletes take Alexander technique lessons to improve the way they use their body. I have personally done it myself for about a year in Switzerland back in 2001-02. AT is not only about having the right posture when you play but also about making the right move with your entire body to achieve an optimal result. It teaches you not to focus on the actual results but on the means to get there. If you do the right move, you'll eventually get the right result with time and patience.
We very often take shortcuts to reach notes or play a difficult passage. Although you might actually get what you want in the short term, you can easily develop bad habits from forcing things which will hurt you in the long run. AT can help you unlearn some of these bad habits and replace them with good ones.
I was always amazed how good my playing felt after each Alexander technique lesson. Some conservatories and music faculties offer it on their premises. If you are lucky enough to be in one of these schools, take advantage of this. If your school doesn't have an AT teacher, make a little research to find one in your area. You won"t regret it. You'll immediately feel a difference in your tone and it'll greatly improve the fluidity of your playing.
Here is a video of an Alexander technique masterclass to give you an idea of what it can do for you. You can find many more about it online.
I am associate principal horn of the Singapore Symphony Orchestra and the author of the progressive methods. I'm happy to share my experience as a horn player and teacher with you.