Hyperparathyroidism can be caused by low levels of calcium and vitamin D. Because you had celiac for a long time, you haven't been absorbing nutrients from your food the way you should. My Mom, who also had celiac had hyperparathyroidism and had surgery for it. After that she was OK.
But you should ask your doctor to test all your vitamin and mineral levels. You could quite possibly be low on others, especially B12.