Cough

So my daughter just continuously has a cough, for months now. I’ve said something to the doctor at every appointment we’ve had. They haven’t been concerned since nothing else has been wrong. Two times it’s been worse with stuffy, runny nose and then drainage and she has puked once each time from the drainage. She is in daycare. My only other thinking is that it’s from the little lovey she sleeps with and sucks on the arms of. We have 2 and I wash them frequently but they still smell musty. Could it be moldy and causing this?