How to get rid of a cough?

My 6yrs old daughter always gets a cough not from being sick but will just start coughing sounds like a dry cough and then she will make herself gag untill I tell her to take a deep breath the cough usually is in the mornings more but will happen threw out the day I have taken her to doctors but honestly I don’t even see they try they always send me home saying she might be coming on to something but I know it’s no I have asked to see a specialist but can’t get to one without a referral has anyone had gone threw the cough with there children before ? She’s always had this problem since she was smaller TIA