Answer: Well, you may not believe this but eating food is associated with choking on food. OK, we all have to eat, so the next thing is reduced sensitivity of the throat. Typically, a person -- a cigarette smoker -- in a steak house is drinking. He takes a large piece of meat, chews a little, it moves back in his throat and he tries to swallow (automatically). He chokes when the piece of meat is too large to be swallowed. Why drinking -- reduces reflexes and cuts sensitivity. Why smoking -- it cuts sensitivity of the throat. So live long by not smoking, not drinking too much (ha), take small bites, and chew thoroughly.
Answer: It is possible that there was irritation or damage to the bronchi or lungs, either from the foreign article or coughing that has caused irritation. If it improves after two or three days, ignore it. If not, see a doctor because there is a possibility that an infection has occurred.
The most likely cause is a muscle strain from coughing that should improve gradually over a period of two or three weeks.