Yes, it sounds like it may already be infected from your description of the dog's behavior. I would ask a vet.....maybe you could find one that would treat your dog 'on a sliding scale'- that is, setting a fee for his/her services depending on your income level.
PLEASE urge them to take the dog to the vet. This is not a situation for "home" treatments. Many vets will offer discounted services. Or the dog's owners can check with the local SPCA for low cost/free services. As dog owners, they are legally responsible for the health and wellbeing of their animal. My parents' cat had the same issue, and had an extremely deep infection that could have led to amputation or death if it wasn't treated. I'm sure you can help these owners do the right thing and help their dog be pain-free. If not, they are liable by law, and should be reported for neglect.
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