On and off I had the same "feeling" for some two years, and still do. A barium swallow revealed no clear answer. Radiologist report said a "possible" aneurism (and he stressed possible as more of a guess). It is intermittently felt, but if I focus on it I may notice it more. My primary care provider (MD) didn't really know what to make of the complaint, but didn't suggest anything further. I take 200mg of Ibuprofen when I note the infrequent pressure. While sometimes I have low pain the Ibuprofen seems to help dissapate it. However, I'm not sure if this is a warning or a non-problem.
Regards, Chuck