N.P.
If the ER doctor missed something as easy to spot as an EAR INFECTION that you can see just by LOOKING IN THE EARS, which is what a good doctor would do when doing a checkup on a kid, I would throw my money in with your pediatrician and dismiss the ER doctor. You've heard the old saying, "If you hear hoofbeats, think horses, not zebras." Right? You probably got eye rolls because your pediatrician found the real cause of your child's discomfort, was irritated at the ER doctor for missing it, and it's not something that would put a black mark on your kid for the rest of her life if it ended up on her permanent record. Time spent with a patient does not automatically correlate to a better diagnosis. A monkey can stare at a math problem for days, doesn't mean the answer he gets is the correct one.
You may have good insurance NOW but let me tell you, that doesn't always last, and having a "pre-existing condition" on your record can completely screw your child and cause her to be unable to afford health insurance if things stay the way they are now when she's old enough to need her own. It's not going to be a mark on YOUR record so it sounds like your pediatrician was just trying to be a good advocate for your child. Another good mark in her favor.
Clear up the infection first before you go nuts about wanting to leave your doctor or marking your kid's permanent record with a diagnosis that could follow her for life. See how it pans out.
I suffered from allergies growing up. Because of this I was always getting sinus infections, ear infections, bronchitis, you name it. The ear nose and throat doctor was pretty much my regular doctor. I used to be a mega wheezer so I can understand how scary it is. They can sound like death rattles. But don't panic, clear up the infection and have your baby tested for allergies.