Hi J.!
My son got the same diagnosis as your daughter when he was 4 months old. They put him on the acid reflux medicine, but I didn't see it was helping and we stopped giving it to him. I kept him propped up when he slept or napped. We took him to an ENT at Hershey, which put our minds at ease, as per our pediatrician's recommendation. She put a video camera tube up his nose and snaked it down his throat to view what it might be (which was awful to watch your baby go through!). However, our Ped. said the same as your doctors, that'd he'd eventually outgrow it. The specialist at Hershey also said it'd probably resolve itself has he grew up and the muscles it affected grew stronger. But to watch any colds in case he needed to go to the ER, in case he needed help breathing. She said it'd take anywhere from 6 months to 4 years til he outgrew it. She said the rattling breathing noise was the loose muscle flapping over the larynx with the air flow And if that flap didn't strengthen on it's own as he grew, then they'd have to do minor corrective surgery. So far he is now 22 months, and has outgrown it so that you barely notice it! My son is now happy, and healthy, the rasping, wheezing, and rattling is pretty much gone! It was tough in the beginning though as it sounded so unpeaceful as he breathed. Then his first 3 colds or so we were nervous wrecks in case he needed to go to the ER. But we never had to take him. I hope knowing that we've been there, and our son is outgrowing it, will help. I found by explaining to our friends and family what was causing the sound, and that it'd go away as his muscle grew stronger, that helped settle them down :) But my son never had respiratory or ear infections either. Just keep checking with your doctors until your mind is at ease. As long as you're are confident with them, then all should be well. Let me know if you have any questions!