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Hello. Thanks for the question.
Dogs don't actually have any sweat glands on the skin. The only sweat glands they possess are in the paw pads and tongue. What you are seeing is edema and oil that is secreted when the skin is irritated or infected. My guess is that there is a skin infection causing the signs. With that in mind, a skin scraping and impression smear is needed to determine the cause. It could be flea allergies, mites, yeast or bacteria. It could also be an auto-immune disease, although this is less likely.
Many of these dogs will be treated with steroids (Prednisone), antibiotics (Cephalexin) and an anti-fungal (Ketoconazole). Treatment for 2-4 weeks is not uncommon in order to get rid of these infections. Once under control, the hair will grow back. I would talk with your vet and get the diagnostics and treatment done as soon as you can.
I hope this helps, let me know if you have any other questions.
You're welcome. Happy to help.
Good deal, thanks for the update.