Something like glass will "bruise" your throat, making you feel like you still have glass in it.  It's like when you choke whilst trying to swallow a Tylenol or something: you'll swear it's still there, even after it's swallowed, but it isn't.  It'll likely go away in a day or so.  If it doesn't, go see a doc.  Hell, go see a doc anyway.  If you talk to the bar you'll probably be able to get in on their tab.
I suspect your body will (not to be too graphic) pack poop around the shard as it digests, so that it doesn't scrape more stuff.  You may not even know if/when you pass it.