If 2 babies (1yo & 2yo) go to doc on same day to same doc, why would they be diagnosed the same bt treated dif?

They both were suspected to have URI's but the 2yo was given an antibiotic and the 1 yo was not. Was told something about needing to develope his immune system. Now the 2yo is doing much better and the 1 yo is doing much worse. Has anybody heard of such a thing? I thought babies developed their immune systems mostly in the 1st 6 months of life. Should we take the 1 yo back to another doc. Has had low grade fever all day and is so stopped up he cant breath. Just sits around and moans all day.