Unfortunately this winter has been bad for a lot of us. I do infant daycare in my home and have 4 babies that are sick and have been for weeks. I sanitize toys/surfaces and wash all bedding weekly, but we can't seem to get rid of this either.
I do not believe your child has pneumonia because all the symptoms sound exactly like what we have all been going through. All of these children have been to their doctors frequently for this round of illnesses. While some have been diagnosed with croup, ear infections, and/or bronchitis, it has not been any more serious than those. If your child gets worse, I would of course suggest another doctor visit, but if he gets put on antibiotics he will most likely develop diarrhea from that and yet the medication doesn't seem to be helping any of the babies in my care get over this any sooner. It actually seems to be prolonging the illness and adding new symptoms. As for it possibly being asthma...doctors will usually not diagnose asthma in an infant this young. They try not to call it that until a child is at least 2 years of age.
Just try to keep your baby comfortable with saline drops, humidifiers, warm fluids to help break up the congestion, reduce dairy type foods and try some clear liquids, etc... And pray for spring!!!