Is the cough
productive;-brings out much sputum, I think your answer is-No!
Then you have got a Hacking cough, It can be caused by many factors but because in your case eating anything precipitates a bout of cough; So I would think of a problem in upper airway rather than down it.
Frequent causes are Viral/HIb Epiglottitis
, Vocal Cord Palsy
, If you are an eldderly then supranuclear palsy, Some benign/malignant tumors of vocal cord region, A Singer's nodule if you are excessive user of speech.
A Otorhinolaryngologist is the right person to be consulted at the earliest.