Skin problems can be especially troublesome, believe me, I understand. We had a household skin problem for several months, and the cat who had it the worst just trembles in fear anytime a stranger looks at her. Taking her out of the house and get prodded by veterinarians several times was horrific for her. On the upside, she feels so much better now that she's not licking herself constantly, and the visits didn't affect her behavior long term.
Getting a Specialist Opinion
We eventually took the family (all four cats) to a veterinarian dermatologist. A regular vet (perhaps a mobile vet who can come to your house) should be able to give you a reference to one if you live near a big city.
If you don't live somewhere that has access to veterinarian specialists, try calling around and finding out if there's a local veterinarian who practices telemedicine. In this practice, a general vet is able to electronically send pictures, xrays, bloodwork, and any other relevant information to a specialist for a diagnosis. Vets often subscribe to these services.
For example, my emergency clinic has access to a telemedicine service. When I took a cat in who was short of breath, the emergency veterinarian x-rayed his lungs and thought it was asthma, but wasn't sure. He sent it to a specialist and the specialist said it was congestive heart failure (it was about 45 minutes from when he was x-rayed until we had the specialist diagnosis). The treatments for the two conditions is completely different, and his responses (and later visits to a cardiologist) confirmed that he really had a heart problem.
Making the vet visit easier for your dog
Wherever you take your dog, make sure that you notify them ahead of time that your dog is terrified of people. A good vet should be able to streamline your visit so that there's less stress on your dog. For example, if you call when you arrive in the parking lot, they can come and get you when they have an exam room available. This allows you to wait in the car (controlling your environment) and go straight into an exam room, bypassing waiting in the waiting room with a bunch of other strange humans and animals. You can also request that the veterinarian does the tasks that the techs/assistants normally do, which will cut down the amount of coming and going of strange humans into the exam room.
With some of my cats I'll take a blanket with me that smells like home, and let them hide in the blanket whenever they aren't being examined. The vets have been really understanding (including the cardiologist who sat on the floor while I had Hunter on my lap under a blanket) to explain his health issues.