I have a sore throat or cough: In general, treat only the symptoms you have, so try to avoid combination medications when one that is for a single symptom could work. Short acting medications that are for less than 4 hours are preferred over longer lasting medications. How you take a medication does matter. Nasal sprays or topical rubs have less of a chance of passing to your breast milk than things you take orally.  

Throat lozenges and sprays are generally considered safe, but avid eating excessive cough drops contains menthol as some have found this can decrease their milk supply. 

Drinking lemon and honey or chamomile tea can be helpful to soother a sore throat and reduce coughing.  Fenugreek tea has also been reported to have a similar effect, although do not drink fenugreek tea if you have a thyroid condition or are on thyroid medications or tend to be hypoglycemic and be aware that it may cause increase gassiness and bloating for you and baby. 

Zinc gluconate or slippery elm bark herbal lozenges may be soothing, but avoid taking large amounts of zinc for more than a week, because it can interfere with other minerals in the body.

Salt water or apple cider vinegar mouth gargles, where you gargle and spit can also bring relief and would not be anticipated to impact milk supply or your baby.

Many forms of robitussin, delsum and benylin are considered compatible with breastfeeding, but always check the active ingredients as there are many versions available on the market. 

Always check with your prescribing physician before starting any herbal supplement or medication based on your unique medical history.