6 month old cough- HELP

Blaire

My (almost) 6 month old has had a cough for a week now. no fever or runny/stuffy nose. when she coughs you can hear stuff she is coughing up, but she just swallows it. just wondering if any mamas have dealt with this. I don't want to run to the doctor if it's not necessary since the flu is so bad right now. I'll also add she has been teething, don't know if that would cause it or not. any help is appreciated