I don’t think these two emotions are bound together, but they do impact us in ways that make us think they are two sides of a continuum. Low anxiety must mean high confidence, but that is probably not really true.
There is some relationship to our family behaviors when we were being reared that impacts us as to confidence and anxiety. If our parents demonstrated high anxiety, we will be more prone to exhibiting that same behavior. If our parents demonstrated high confidence, we will tend to be more confident.
If you have problems performing due to feelings of anxiety when you try to stand and speak, or find yourself struggling to do your job as you feel a lack of confidence in your ability, then you may need to spend some time with a counselor (maybe your pastor, or a licensed therapist depending on which you would trust more), and try to get to the root cause of the behavior. Do not blame yourself, or anyone else as this is something that can be overcome with help and assistance of a good counselor.
Another really super thing you could do, if you can get past the fear of letting go, is NLP (that is neuro-linguistic programming). NLP is akin to hypnotizing, but more clinically controlled and has a record of really getting results in changing behaviors.