This career is about overcoming and adapting. Using all available resources and thinking outside the box is a necessity whether in the cockpit or navigating the ups and downs of this industry.
Have you asked yourself what it might take to overcome this phobia? Have you seen a counselor or a school advisor? Have you seen a psychologist? Have you taken a public speaking class? I can assure you that working on your CFI in a professional environment amongst fellow CFI candidates will be a positive experience. Constructive critique should be welcomed and expected, but you will also certainly find some support and comraderie as well.