I know when I was job hunting it was very stressful.
I don't think you can completely get rid of the feelings of insecurity. They are real and they are there. I think just recognizing them for what they are is a good thing but not to let them dominate and leak into other aspects of your life is the tricky part.
I think taking the time to think about the positive areas of your life. Your sobriety and going to AA. If you have not, you could bring up the stress of job searching at an AA meeting if you go to one that has an open discussion. I am sure others are in the same boat. You never know where a job opportunity may arise.