Long cough and runny nose

My baby, 7 months old, is having runny nose and cough on going for almost a month. And seems to me that it is not going away. Similarly, he has been on the medication for a month long. After a doctor's consultation, he advise to continue with the medication (does not include antibiotics) until he recovers. But I am starting to get uncomfortable with the continuation of medication. Because I am fearful of the effects of taking these meds for too long, and he might be even addicted to it. Dear mummies, what is your advice? Thanks.