Wow, that sounds really dreadful. We do have allergies in our family, but haven't had a reaction exactly like that. Hives tend to go away as soon as an antihistamine is taken. Rashes do frequently last longer. In reactions to food, I would say a severe rash might take five days to go away. I've had bad reaction from plants (ivy) that has taken four weeks for the rash to go away. In one case, it was so bad, I had to go on a steroid (prednisone).
Is it crusty because of scratching? The absolute most important thing is to not scratch it. It could get infected on top of everything else. There are stronger meds than Benedryl. I would ask your ped. A warm (not hot) bath, followed by a lotion (like Cetephyl) will help keep it moist. Be careful, though, because many lotions might sting. I found that sometimes a cool compress helps. However, since it's his whole body, that won't work. Maybe try it on any particularly itchy spots.
Also, although allergies are genetic, it is a general susceptibility that is inherited. So, if anyone in the family has ANY allergy, to foods, pollen, dust, pets, bees, etc., that would qualify as a family history of at least some allergies.
Good luck!
D.