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They commonly get nailbed/toenail type infections that can cause swelling and be painful. The infection can be mixed between bacterial and fungal...and much like us, nonresponsive to topicals and require oral medications. And as always, I feel a vet visit will yield the most affective medications.
IF you are reluctant to go to a vet. For now you can start with diluted betadine soaks (drug store) it is brown and will stain the foot...you can ask for a chlorohexiderm solution that doesn't stain. Regardless of bacteria or fungal the solutions do help. You would soak the foot twice a day for about 5-7 minutes. Dry well and you can purchase a topical antifungal spray or drops or cream. Apply this for 2-3 days. If you don't see improvement you need to go to a vet.
The hair will fall out with the infection bothering the hair follicles AND the chewing of the dog.
The other thing we look for is localized demodetic mange...that also presents like this.
As I stated..the vet can look, and when I see these I almost always reach for an oral medications...but we still do the soaks and topicals.