I am not aware of a cortisone based shampoo but I do have some suggestions.
There could be several things going on here. First and foremost, you need to get the dog on a prescription flea remedy to rule out a flea problem. Frontline is my favorite and it can be bought over the counter with no prescription.
Your dogs could have allergies to fleas. If this is the case, it only takes one to get the itching started. Even if you don't see fleas, it only takes ONE BITE to get the cycle started in a dog that has this allergy.
Your dogs could also be allergic to products, the environement or food.
If you can't get this under control, you really need to talk with your vet about a low allergy diet, antihistamine use, and a steroid to help curb the itching and give the skin time to heal. Steroids can give the skin time to recover from the itching and allow it to heal. Your pet also might have a secondary bacterial or fungal infection. This is pretty common when there is this much itching going on.
Lastly, you will want to have the vet scrape the skin to rule out deomodectic and sarcoptic mange. One is contagious and the other is more of an immune disorder. They do not have to be exposed.
I also suggest that you get him started on a supplement that contains omega three fatty acids. Good skin starts from the inside out.
Let me know if you have more specific questions about this.