I always feel as 'though there is a piece of food stuck in the back of my throat.  I read an article online about tonsil stones and it seems like it could be that.  It can cause slight choking at times, hard to swallow, although the swallowing part is OK.   I ordered one of those medical flashlights with batteries to check my tonsils, see if I can see anything before going to a doctor about it.  It does not bother that much, but is just a bit annoying.