Seems to be an allergic cough

cough after exposure to cold food, night time cough,repetitive cough, history of allergy in family: these r typical of allergic cough

it appears to be allergic cough/cold. they can be associated with temperature variations around the body (hot to cold or cold to hot environmental changes) which the body cannot sustain leading to cough usually at evening /night and morning. requires examination and start anti allergic medicines. meet dr and prevent such temperature variations. there is a possibility of starting anti allergic medicines for at least one month and the doctor will decide if the child needs inhaler therapy or nebulization.

Need more details regarding the history