that's why my first concern was about a bone splinter. that can turn nasty quick. if you can find the bone and see that it is intact, no worries. just wait it out and see. if the bone has a big splinter or a chunk missing, that's when i would get to the vet asap.
if you ever worry that your dog has swallowed something, you can always make it barf by giving it a tablespoon of salt. they don't like it, but it works every time. clearly in this case that is not applicable.