If it's not bacteria related, antibiotics will not help anyway. In fact they will weaken his immune system and make it worse. That sounds like a smart doctor....
There are things that will help his immune system and his throat while youre letting it run it's course. Elderberry syrup or extract will build the immune system. You didn't say how old he is but you can get it in liquid and it tastes good so it's easy to give. High grade tea tree oil diluted in water and gargled will heal and bring down the swelling. I use a throat spray with the oil in it and it somewhat deadens the pain as well. You can put the tea tree oil in a vaporizer as well as it is aromatic too. That will help his breathing. An absorbable multivitamin will help so the body will try to fight it off all by itself.
If you're interested in other ways to build the immune system and want to go that route I'll be glad to elaborate for you. Let me know.