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.