The best Over the counter medicine for breaking down a cough is mucinex. It loosens everything and makes it productive shortening the length of your illness. Another good expectorant is Robitussin DM. You don't want to just suppress it if there's something to get up. The latter stages of bronchitis usually entail breaking up of mucus in the chest. Another thing to maybe try is a warm cup of lemon tea. It's just very soothing. Usually when I'm sick (other than antibiotics) I use a eucalyptus scrub and warm tea. Oh and someone once told me you can smear vicks vapor rub on your feet and put on socks and it stops the coughing asap. That's one I've yet to try.
So sweet your baby is worried about you
Hope you feel better