Well, teaching is not exactly a stress free profession but, there again, which one is?
I believe you will need to provide a clean bill of health in order to get your visa so if your condition is a clinical one and it has been recorded as such on your medial records than you might have a problem.
However, if your anxiety is a manageable one and you believe you can control it then I don’t think you would need to mention it in your application.
With regard to a stress free training program, you may want to consider an online course as opposed to an on site one.
You can find good online courses that provide quality training and allow you to work at your own pace. Having no deadlines but those which you set for yourself is a great advantage.
Working on a course with a flexible schedule where your personal tutor can be contacted 24/7 or your coursework can be submitted whenever ready has allowed many of our trainees to complete successfully their TESL/TEFL Certificate course, further their knowledge and gain better prospects of employment.
I hope this helps