https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5315033/#!po=62.2807 Here's an article that looks at hair loss due to nutritional deficiencies.   Celiac Disease causes malabsorption which results in malnutrition.  The B vitamins all work together.  You might benefit from taking a B-Complex vitamin like ravenwoodglass suggested.  My hair thins out if I don't get enough Niacin and Zinc.