Child With Left Ear Pain, Cold, Severe Congestion, Whooping, Ear Dark, Inflammed From Inside. What Is The Solution?

my 9 year old daughter came down with ear pain (she described it as a knife stabbing ) in her left ear. It looked red, inflamed, and a lot of wax build-up. the next morning she woke up with severe congestion and whooping cough , but her ear pain had improved tremendously. She went to her pediatrician (not her regular Dr.) and after 3 minute exam she was diagnosed with a cold and the beginning of an ear infection so they prescribed Amoxicillan. I do not feel this is a correct diagnosis. not sure how ear pain (w/o any cold symptoms at all) can miraculously turn into a cold as the primary issue and the beginning of an ear infection as secondary. I looked again last night in her ear and it was super dark, inflamed, and swollen with lots of black stuff. Tried to identify her tympanic membrane but either the canal was so swollen the shadows were preventing identification or i am concerned there is a rupture. Any opinions?