Is it possible to get little pills stuck between your nasal passage and your throat. And can it burn your throat if not swallowed. Ibuprofen.

Yes definitly. Aspirin, ibuprofen, potassium pills and others can cause small ulcers. In some people the pills get stuck in the tonsils but some people have pockets (diverticulae) in the throat or esophagus and some people have narrowing or spasms in the esophagus. The enteric coated medications are designed to dissolve lower in the GI tract. Try that. If it is a problem you should see a gastroenterologist.