Hello and welcome to the forum. As you know, the food that your vet recommends is a hydrolyzed protein type (there are several on the market). They consist of a single protein source that is processed to break the structure of it down into tiny particles that the dog's immune system will not recognize as an allergen. The carbohydrate source is usually one that the dog is unlikely to be sensitive to. I assume that the reason this was recommended is because at the moment you do not actually know what your dog is intolerant of. Sensitivity tests can be done but I would imagine they are expensive and AFAIK not always accurate. The idea behind these products is that the dog starts out with it then very slowly different food types are added, one by one to elicit the dog's response. It takes a long time and needs to be done carefully with strict attention to diet (no treats).
As you are not keen on this type of product I think you should consider a good quality wet food. The reasons are:
1. They usually have a much simpler formula than dry food thereby reducing the risk of intolerance to ingredients.
2. The risk of storage mites is much reduced - link
. In a dog that is allergic to these critters, they can cause all the symptoms that you describe.
Alternatively you might want to consider a raw diet. However, you will need freezer space. Also, unless you feed one of the raw complete products such as Natural Instinct, Nutriment, Natures Menu (there are more), you will have to do some homework to get the correct balance of muscle/organ meat/bone and vegetables. There are plenty of Facebook groups that can help you with this and there is a lot of information on the Internet.
If you are minded to try a wet diet I would suggest that you go for ones that have a single source of protein and that you keep the dog on that one product for at least one or two weeks with nothing else being given (including treats). This is the only way you will be absolutely sure of the dog's response. Once you are sure the dog is OK then you can try another type of protein. The Dog Food Directory of this website is useful for narrowing down the search for suitable wet food products. Normally the advice is to choose grain free dog food and there are quite a few in this category. However, there are one or two good quality products that contain white or brown rice and they might be helpful here because although a few dogs cannot tolerate rice, most are OK with it.
The company Naturediet have plenty of fact sheets about the issue of intolerance and might be worth considering. One of them is here
and their website is here
. Their sensitive version is made from salmon and very few dogs are allergic to fish. It does tend to be a bit smelly but the dogs quite like it for that reason.
Don't overlook the fact that as your dog is scratching there is always the risk of bacterial infection of the skin. If it is red and inflamed, see your vet as antibiotics may be needed. Also consider medicated baths. You could ask your vet about this but I have heard that Neem is recommended. I have used Selene for eczema and found it helpful. Sebocalm is a gentle, soapless shampoo that hydrates the skin and may be helpful.
Please post back if you require further help and we would be grateful if you could let us know how you get on with your dog's problem.