So sorry to hear about your struggles. I hope I can help in some way. (not medical advice and I'm not a doctor, but I do value real science)
From what I understand, zinc is one of the most reliable/effective things to treat coughs/colds. Echinacea is fairly good to try also.
Also, as a sort of "folk remedy" that my parents did was to mix sliced raw onions, fresh/raw lemon juice with raw honey, put it in a regular size pitcher and let it sit over night (covered in plastic wrap or a lid that sealed, so as to contain the smell, etc.) in the fridge to kind of blend/ferment/mix together and the (strained so it didn't have bits of onion in it) juice it made tasted mostly okay, and even kind of tasted good, and would really cut through mucus/knock out any colds or coughs we would get as kids.
There were 5 boys and one girl in my family and so my parents needed to make a lot of cough medicine if a lot of us got sick at the same time. (and this was much cheaper than cough medicine from the store.)
It was basically home-made cough medicine that I personally experienced as working very well and usually fairly quickly. (if you want to skip the onion/fermentation/overnight part that is fine.) Lemon juice or honey individually or put together are both very good to kill off bad bacteria/viruses and clear out mucus, etc.
Here is some (well-researched) information on what things are snake oil and what things are actual vitamins/herbs/plants/minerals/supplements that are more or less strongly supported by (valid, measured, more reliable) scientific studies to have shown real benefits for people's health depending on what specific thing ails them:
http://www.informationisbeautiful.net/subject/health
I hope you and your baby feel better soon. Take care. :)