ToothDK and Nancy T have the right idea, go to the ER.
After swallowing a foreign body, many people still can feel a foreign body sensation in their throat, especially (sometimes painfully) when swallowing.
If you are able to localize the foreign body sensation precisely above the adam's apple (thyroid cartilage) that implies a foreign body in the hypopharynx your may be able to see with a mirror and headlamp
Some people can only vaguely localizes the foreign body sensation to the top of the sternum (suprasternal notch) which could imply an foreign body anywhere in the swallowing tube (esophagus).
If a person is coughing and wheezing then doctors would worry it's in the windpipe (tracheobronchial tree) .
If a person is drooling and spitting up of whatever fluid is swallowed then we worry about obstruction of the swallowing tube (esophagus)
If your symptoms are mild, your doctor may test your ability to swallow, first using a small cup of water and then small piece of bread. If the bread does not eliminate the foreign body sensation we'd be worried it's still there.
Your doctor may use a mirror to look in the area you descibe as being uncomfortable.
A scratch in the throat can produce a sensation that the foreign body is still there, but in reality isn't.
Further endoscopic studies can help evaluate continued symptoms, an otolaryngology (ENT) referral and consultation can help with this
Go to the ER. That small bone can get lodged someplace else after it falls out. Either go to the ER or go to your doc when you can.
Wish I knew what to tell you, but I must commiserate. I accidentally (mindlessly) swallowed a huge salmon bone once. The barbed end lodged firmly on one tonsil, and the bone was sticking straight across my throat and poking my other tonsil with the sharp end.
I could SEE the darn thing, shifting in front of and behind my uvula ("punching bag") when I'd try coughing it up or washing it down. I tried for a couple of hours and finally called the doctor. When they didn't call back (a Sunday evening), I went to the ER--stupid, but that sensation of a large fishbone poking into both tonsils was becoming unbearable!
I thought about trying to pull it out with tweezers, but was afraid I'd drop the tweezers down my throat and then I'd really be in trouble.
I doubt it will go into your lungs, and if it went down your throat, I presume your stomach juices would dissolve it like they presumably dissolve all those tiny fish bones we swallow.
But I would highly recommend you go to your doctor and have them take it out. So it won't bother you or possibly get infected. At least call your doctor and ask what you should do.
Good luck!!!
Nancy T.