cough and cold for 3 weeks and probable without fever as you have not mentioned is most likely allergic and your doctor has given you some antiallergics which have not helped you.see if ther is a family history of any allergy like skin allergy or respiratory allergies like recurrent sneezing or coughs then your childs cough needs to be evaluated .check the childs nose and ears as an ear infection can also cause cough,is the cough more in day or night ,does the cough increase early morning or late night,is the child feeding well or not all these need to be looked into.

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Hello.. Well my dear I understand that you are apprehensive about your child but then I would like to tell you because of the weather it is right now ..Its quite possible that he doesn't get well in a day...Continue the medication for 3 days atleast...Make sure she is active and feeding well...Her injection is also due..So you an consult a paediatrician if symptoms doens't subside in 5 days or she becomes dull, stops feeding...Thank you