Hi thanks for contacting health care magic. Cough after meal can t usually by thyroid problem... You can consult physician for examination with keeping below suggestion in mind... First it could be by certain food allergy like that of peanut, egg , milk , citrous fruits etc..... Excess beverages can lead it like alcohol, soft drinks etc.... Second acid reflux disease can be the cause. In which after meal acid travel back to esophagus and cough. Sometimes viral and bacterial throat infection can lead it... If needed hiatus hernia has to be ruled out by barium study. Meanwhile eat slowly. Avoid excess spicy. Hope your concern solved.