My 7yr old has been coughing a lot and throws up phlegm. How can I help her? No allergies has been tested. Has asthma. Had GERD as baby dr said she outgrew

See below. Coughing and gagging up the mucous is actually good! your child is clearing her throat and lungs and this is protective. If anything, give an expectorant (mucinex) and decongestant (sudafed) and then, sit her up, humidify the air and have the child spit out the mucous.
Asthma control. The persistence of cough with phlegm may indicated that your daughter's asthma is not under control. Adding an inhaled corticorsteroid or singulair (montelukast) may be appropriate. Gerd could be a factor and a trial of therapy could help. Other considerations would be persistent bacterial bronchitis or pertussis (whooping cough). An evaluation by an allergist would be appropriate.