What should I do? My son has runny nose and now greenish mucus and cough for 10days now

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He is still the happy baby but his cough is getting less as well but still coughing. I called the nurse line and told us to check in. I told my husband if he wants too since we are anti medicine. And my husband says no and says if he thinks its necessary to check in they will just give our 1 year old an antibiotics. What should I do? I just wanna make sure my babe is okay.