Skin crusts and bald patch! Please help!

Hey there. I have a six year old Cockapoo that's suffered from skin issues all his life. They range in severity and duration. Sometimes he goes months at a time with no issues, sometimes they reappear after just weeks or a month. He develops these yellowish skin crusts/scabs. They cause him to itch and they have a fairly strong smell. I have him on omega-3 pills and Hills prescription diet dog food z/d for skin sensitivities on vet's recommendation. They help, but haven't solved the issue. For years I've taken him to the vet only to have him issued antibiotics, which only solve the issue temporarily, or told that he'll require extensive allergy testing that could cost nearly a thousand dollars in total.

His latest issue is occurring underneath one of his ears and it's causing a bald patch like I've never seen before. I'm sick of not getting a conclusive answer and have decided it's time to go to the internet for some possible answers. I'm attaching two images of the latest issue. Any insight into a possible diagnosis/solution is GREATLY appreciated! Thank you so much for your time!

It could be a yeast infection. Has your vet done a skin scrape??

There is a whole load of rice, grain and corn in Hills feeds, (grain and corn covers a multitude of products).
It is well know these days that our very modern and convenient dry kibbles are causing a lot of allergies and general health problems for our pets.
Have you considered a complete change of diet ?
My suggestion would be to change to a completely raw diet. This is so natural and easy for our dogs digestive systems to digest. It is well reported to solve many skin issues and general health improves too.
Feeding raw does not have to be messy or bloody, there are many pet stores these days who have freezers and sell frozen dogs meals.

There is a nice book by "Kymythy Schultze" , which is easy to read and understand and it may help you make a decision "Natural Nutrition for Dogs and Cats".
It can be purchased on Amazon for 1p ( used book as new)

Make sure his flea protection is up to date

Try him on an elimination diet - change foods to something like salmon and potato to take out all of the proteins he is used to. Every four weeks or so, add another food type for a month to see how he reacts

Keep a diary so that you know what foods you have given and where you have exercised him

It may save you the cost of allergy testing

Cooked meats and processed kibbles are totally different to a raw product. Raw meat products are not affected or altered by cooking or processing, and reactions can be totally different !
There is also a poor/cheap protein in grains which is not natural for our dogs 52 weeks a year, although many dogs manage them perfectly well.

In my experience of yeasty type skin problems , they are almost always caused by feeding dry kibble type foods which due to the excess carbs cause bacterial overgrowth on the skin, leading to fungal infection and odour. I would strongly recommend a change to a raw diet - as advised by Forgotten. At the very worst it will cause no harm, and will most likely solve the problem without resort to expensive veterinary treatment. Good luck!