Hi Julie,
Allergies are indeed a known trigger for Graves' disease. When we have allergies and we're exposed to the allergen, our immune systems react. In doing so, they produce immunoglobulin E. Numerous studies show that high levels of IgE are associated with more severe symptoms in Graves' disease. In Japan, allergies to cedar pollen are considered a major cause of Graves' disease. Most people with Graves' disease have a combination of environmental triggers that contribute to their disease and influence symptoms.
You'll probably notice on your box of Allegra-D that it says this product shouldn't be taken by people with thyroid disorders. This is because a certain class of drugs called sympathomimetic amines (ephedrine, pseudoephedrine, amphetamine, methamphetamine, etc) stimulate the nervous system. So does thyroid hormone. So any symptoms of hyperthyroidism can increase with drugs of this class.
You could take Allegra only--it doesn't contain pseudoephedrine and the other ingredient is safe, or Claritin. Most of the newer allergy meds are safe but Allegra-D isn't. Nasal steroids are excellent because they inhibit the allergic reaction locally and have few systemic effects. If your hyperthyroidism is in very good control and your thyroid hormone levels are low, your doctor might feel that Allegra-D is safe. If you're newly diagnosed and have high thyroid hormone levels, this wouldn't be the case. You can always call your doctor and mention you noticed thyroid disease mentioned in the product information and ask if there's another medication that might work better.
With more deaths caused in U.S. hospitals caused by medication errors than certain diseases, it's always wise to check for potential side effects and drug interactions. It's good that you're researching things. Best, Elaine