Never heard of pneumonia being "mild". That's called "bronchitis".
a 105 fever is a few degrees away from brain damage.
I had pneumonia repeatedly when I was a youngster, between the ages of 7 and 14. I can recall one occasion my dad rushing me late night to the hospital in a Vista Cruiser (no shit, for real) on a CB getting a police escort (those were the days...now they'd call a swat team, shoot your tires out, break your arms, jail time, ...), and the cop was there in a heartbeat, we're both flying down the highway to the hospital. The cop complimented my ol' man on his driving, wished us well, and drove off after seeing us to the Emergency Room door.
I was in an oxygen tent for days. Blood tests drawn every hour. Took days before I was released.
I couldn't breathe except for in very VERY shallow breaths or I'd go into a coughing fit and be unable to stop.
Pneumonia is VERY SCARY REAL SHIT....
I'd consider going to a second doctor after getting your son admitted to a hospital, stat...no fucking around.