It is likely an allergy, but your vet should be giving 4 weeks of antibiotics along with the steroid shot, or this will not heal properly. In addition, they should be ruling out mites or other parasites by skin scraping. This will tell them if there are mites, and also wether the infection is primarily fungal, bacterial, or a mix of both. Then they can give the appropriate medications-both topical and oral.
Skin conditions due to allergies (this sounds like it is) are generally hard to cure. They are usually only managed.
Talk to your vet about management of allergies, or find a vet who can truly help your dog's with this.
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If you are bathing them with the right shampoo, twice weekly is what I recommend. I am not familiar with the shampoo you mentioned. Depending on the infection (bacteria vs yeast) I recommend Malaseb or other veterinary products.
The Clavamox is old, throw it out. It would not have been my first choice for a skin infection, and as I said...4 weeks of antibiotics to heal the skin. Any shorter, and the infection tends to return. Many vets do not treat this long, but it is what the dermatologists recommend.
You can either keep a shirt on the dog, or booties on their feet.
Malaseb is a shampoo.
I use a cephalosporin...there are many types, and your vet should use whatever they are familiar with.
Your vet should scrape the skin to find out if there is yeast/bacteria. This is simple to do, and they look at the scraping under the microscope.
Dog Veterinarian
20 years experience in veterinary field.