It sounds like your dog might be allergic to flea bites. If one of your dogs has fleas and ticks you can be sure the other one will have them too unless the other dog has been protected by medication.
For fleas you might try Sentinel - it controls fleas and ticks and also protects dogs against heartworm. You inject this into the dog every month (it's just a small injection). The amount used is based on your dog's body weight and (I think) you can only get it from a vet - that's how it is in Canada, where I am. There is also Revolution but you can't bathe your dog for a few days after using it.
You can get spray from your vet to spray where the dog sleeps or spends a lot of time. This should get the fleas off your dog and her living space.
If you have any further questions, please let me know.
We had a problem once with the flea shampoo causing severe irritation and rashes. These shampoos often have an insecticide in them. You might try immediately switching to baby shampoo, or one that your vet recommends, and use an anti-flea medication recommended by your vet. You might be able to kick-start the flea killing with Capstar tablets, which kill fleas pretty quickly, but are not used for long term control.
The fleas themselves can cause an allergic reaction, and one dog might be more susceptible to this than the other.
We have been using Sentinel, which is an oral combination of a heartworm preventative, and a drug that prevents flea larvae from developing. It doesn't kill adult fleas, but we have broken the life cycle and we never see fleas. There are also topical drugs that are applied to the neck that will prevent heartworms and kill adult fleas.
It could still be something else, but if it were me, I would rule out the harsh medicated shampoo first. Maybe the docs will have better recommendations. Good luck - hope you and your pooch get some relief!
My mistake. Sentinel is a pill and according to our vet it does kill adult fleas as well as flea "eggs". Capstar is good at the end of the month when the Sentinel is wearing off. Our Akita is allergic to fleas so I can relate to what you are going through.
The vet would know better what to recommend.
It could be a few things. First off only 1 type of mange is contagious (sarcoptic aka: scabies) It could be demodectic mange or a bacterial infection which needs to be dealt with asap! Either way get to a vet. They need to do some deep skin scrapes and view them under the microscope to see if it's demodex. Depending on your dogs breed type they can treat with either ivermectin or dips. It is a long treatment but necessary for quality of life! Bacterial infections of the skin can be caused by allergies and are often misconstrued as a rash by lay people. They should be treated with oral antibiotics and cephalexin is a good antibiotic to ask for to be called into your local walmart pharmacy because you can get it under walmart's $4 generic list to save yourself money. If it's allergies then pinpointing the cause is key to management of the allergies. Please look for my previous posts on allergies for tips. Good Luck!