They just wont do NOTHING!!! 4 yrs old

I wish i could just have 1 doctor that actually cared .. My daughter was sick with a cold around 2 weeks ago (runny nose,cough,mucus) a little bit of everything on the 6 to 7 day she was good already except she had a cough still so ok i take her to the ER because it got worse one night Which they dont do nothing but say its alot of mucus trapped in there so i Start giving her MUCINEX for kids which ended up being in the hospital on the second day because she started bleeding ALOT FROM HER NOSE AND MOUTH "called 911" they said she was very dry plus i had the heater on (to stop giving her mucinex) 3 days later i take her to the ped she got an appointment to see a specialist for the blood still today 3 weeks later and shes still coughing every time she runs jumps on goes out to the cold.. Doctors keep saying its a dry nose connected to throat and that its normal I KNOW IT IS NOT NORMAL SPECIALLY WHEN SHE CANT EVEN JUMP 1 TIME WITHOUT COUGHING but they dont care ive went 2 times already and still😭😭