You are having cough for 5 months and took cough syrup
as well some antibiotics . You got some relief but cough still present , particularly when take milk , ice cream ( milk products ).
Such type of cough may be due to these possibilities , these include:
to dairy products , particularly , you mentioned that you develop cough after milk and ice cream . Diagnosis can be confirmed by allergy test for milk products . So consult an allergy specialist and get allergy test.
2 The next possibility of such symptoms may be due to asthmatic allergic bronchitis
( in this condition patient develop cough due to bronchoconstriction
caused by allergy by mold, dust, pollen, fumes , smoking
) So take care about these allergens.
3 Smokers cough , if you are smoker then this cough may be due to smoking.Be careful about that also.
however , there are so many other reasons of such cough but consult another physician and get his opinion as mentioned above.