An allergy to gluten, which is not an allergy at all but actually gluten intolerance, is not the same as celiac disease.
A food allergy is a reaction of the immune system to a food that is deemed dangerous to the body. Intolerance is a reaction of the digestive tract. Celiac disease is an autoimmune disorder, in which the immune system attacks and tries to destroy the body's own tissues. In the case of celiac disease, the immune system attacks the small intestine.
The symptoms of gluten intolerance and celiac disease are similar; gluten is a protein found in wheat and other grains. These symptoms include gastrointestinal problems, such as abdominal pain, gas, bloating, constipation, diarrhea, nausea and vomiting. The symptoms can cause weight loss, anemia and under-consumption or malabsorption of nutrients, as well as weakness, chronic fatigue and memory or concentration problems.
In addition to the gastrointestinal symptoms, gluten intolerance and celiac disease can cause skin irritation, headaches, joint pain, muscle cramps and neurological complaints, including tingling or numbness in the hands and feet, and even seizures. They can also cause irritability, behavior changes and depression, as well as infertility and fetal loss.
Your doctor can test you for celiac disease by doing blood tests for antibodies. If the blood tests suggest that you might have celiac disease, your doctor will have to do a biopsy of your small intestine for confirmation. There is no test for gluten intolerance, so to find out if you're gluten intolerant you'll have to do an elimination diet and then slowly reintroduce the foods one at a time until you figure out which ones are causing the symptoms.