It could be eczema...that's what both of my daughters look like when they have a breakout of it. Especially since you mention the allergies. It may not be bothering him, but you ought to treat it before it gets worse and does start to bother him. A side note...both Aquaphor and Eucerin makes my daughters' eczema worse...so does Vanicream. The only lotion I've ever used that worked is Johnson's Creamy Baby Oil, and for treatment cortisone never worked, but a prescrip. cream called mometasone did. Because it sounds just like theirs, you might try it to see.
And totally just curious...you don't use any soap on his body? It could be that he's getting some sort of skin condition because he's not being cleaned. I don't mean that to sound facetious or sarcastic...I'm serious, in the most polite way. At that age, he has to get dirty enough to require actual washing. Water is just drying, and doesn't do much.
***EDIT Thanks for clarifying. By soap, you probably shouldn't use normal soap...but have you tried Dove, or Cetaphil, or something like that? Dove was the only soap that didn't make my oldest break out immediately, so I used that until she was about 4. It could be that he's become sensitive to the soap you are using...as sensitive as any soap claims to be, skin can become sensitive to it after repeated use.