So many people go to the doctor looking for antibiotics as they are not willing to let a minor illness run its course. Of course there are some things that antibiotics can help and others that they can do no good for.
I have always been very clear with our pediatrician (and my own doctor too for that matter) that when I come in in a situation like this, I am just looking for them to listen to her lungs, check her ears, etc. and assure me I am fine to go ahead and let the illness run its course. I am always clear to say that I am NOT looking for antibiotics unless they are NECESSARY. I have had the discussion with him that I fear they are overused and don't want to do that but am happy (well, not happy exactly, but willing) to use them when they are really needed. So far, he has been great. We usually get the "it will run its course, lots of fluids, etc." talk but on occasion have had the antibiotics prescribed and use them then.
I have heard varying reports about green mucous from the nose. That personally worries me a little so especially with the icky cough, I would pry go in for a little once over. If the child is eating, sleeping and acting fine, I am always less concerned than if these are affected.
Hope all are healthy at your house soon!