Flattened villi can be seen in other conditions besides Celiac. Eosinophilic Gastroenteritis is one such condition. See www.APFED.org
for more info.
Eosinophilic Esophagitis causes reflux-like symptoms and food getting stuck/choking. Eosinophilic Gastroenteritis can cause flattened villi and may or may not have other symptoms (nausea, abdominal pain, diarrhea, etc.).
It would be a good idea to discuss food allergies (milk, wheat, corn, soy, egg, tree nut, peanut, fish & shellfish are the most common) and environmental allergies (tree/grass/weed pollen, dust, animals, mold, etc.) with your doctor, as food & environmental allergies are known triggers for gastrointestinal or esophageal inflammation in those with Eosinophilic Gastrointestinal Diseases (EGID's).
Other conditions that can cause flattened villi include food allergy/sensitivity/intolerance, Immune Deficiency, gastrointestinal infection (giardia, TB, Whipple's, etc.), Tropical Sprue, HIV, Autoimmune Enteropathy, Radiation Enteritis, Crohn's Disease, Intestinal Lymphoma (which may be associated with Celiac), Zollinger–Ellison syndrome, etc. Basically, anything that can cause chronic inflammation in the gut can cause flattened villi.