Its quite possible that somewhere along the line your puppy came in contact with something that caused this reaction. So maybe it is just a contact allergy, You really are not going to know if its a life long allergy until it presents itself again. At least you are better prepared if there is a next time.
The shampoo you were told to use, probably exacerbated the rash. Sometimes its not a great idea to bathe a dog who has a rash for fear of spreading it. There is also the possibility of stripping away the natural oils on the skin which will make the rash itch more. Maybe the rash that your dog experienced was something that was spread similar to how poison ivy is spread on human skin.
We think its great that you actually found a competent vet. If you do not mind we would like to know the actual names of the antibiotics that were used. We would like store this information away just in case we have a similar experience.
Sometimes, owners suffer as much as their dogs when they see them in discomfort. Have faith, maybe this will not re-occur.