hi there, your food seems to have entered the larynx
or the wind pipe as food pipe and the wind pipe are in close proximity and it is the natural defence mechanism of the body to cough
to dislodge the particle from there. As you have stated coughing for 30 min has left the larynx sore and it gives a sensation as if something is stuck there. You should try a avoid the urge to cough if you have got the particle out of your throat and take an anti-inflammatory to reduce the inflammation. In a day or two you will be fine. Do make a habit not to talk or laugh while eating as the food may go the wrong way and that can be troublesome as you have already experienced . Take care.