My dog got a giant sore hot spot, went on for a month or two, the vet didn't really help, and it turned out he was allergic to peanut butter. Of all things. So sometimes it's a really random substance.
I don't wanna give medical advice on here, but if my dogs have mild allergies/are itchy for no discernible reason, I give them Benadryl (diphenhydramine) which is generally considered safe for dogs in low doses, the guidelines for which are readily available on the internet.
That could be it. Try removing the straw and see what happens . Why dog was balding around his eyes due to an allergic reaction to his food the vet warned us of straw, hay, change in food, tumbleweeds, and other plants.
Maybe its a "hot spot" i've seen hotspots and this sounds almost like them. "Redness, oozing, pain, and itchiness are hallmark signs. Hair loss is commonly present. Sometimes hair can mat over the lesion, obscuring the size and degree of the problem. These lesions can appear suddenly, and grow rapidly (hours).
It is common for an owner to notice a small area of inflamed skin in the morning (perhaps an inch or couple centimeters in diameter) and come home from work to be met with a large area the size of the palm of a hand. The dog is usually highly agitated, and will not leave the area alone. Some dogs will even growl or snap if the area is touched." - [link]
It could also be mange mites, which would suck. As for fleas, there are different species of fleas and some of them will only feed on certain types of mammals, so the dog having them while the cats don't isn't completely odd for a flea infestation, depending on what kind of flea. It could also be an allergy, dogs like labradors seem especially prone to food allergies and allergies to household cleaners. If it's an allergy, you might think about changing your dog's diet to one with more meat and less wheat/corn in it if he's on dry food. These plant fillers often trigger allergic reactions in sensitive dogs.
All I can think of is fleas, maybe ticks. I don't know, but something obviously is messing with his skin.
I just searched some things up of what can cause scabs appearing; fleas, mites, ticks, an allergy, certain shampoo's, lack of something in the body. Maybe this can help, sorry if it doesn't. Did you change anything? Different food or something?