What could cause throat pain (above & to right of adam's apple) when tilting head back? Have had lump there when swallowing but MRI showed nothing.

ENT+GI docs to check. If something is in the throat or neck, an ear-nose-throat doctor and a gastroenterologist should evaluate. The doctors can decide if it's worthwhile to do a cine-esophagram or other swallowing study to see if something happens during swallowing. Sometimes, nothing can be found at the present time, but rechecking later may locate a problem, especially if the problem has grown big enough to show up.