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Your dog clearly has an ear infection and needs proper veterinary care.
Unfortunately, many ear infections are not treated as seriously as they should. One of the problems is that the external ear canal of dogs has two distinct sections, the vertical (outer portion) and the horizontal portion next to the ear drum. You can only see a little way down into the vertical ear canal, and you cannot see the horizontal portion without the use of an otoscope (the instrument used to look at the ear drum). Too often, veterinarians diagnose an ear infection, send the client home with medicine and fail to recheck the ear(s) when the period of treatment is over. Many times, the medication will quiet the infection in the vertical ear canal, and provide some relief at the level of the horizontal ear canal. But, if any debris or infection remains in the horizontal ear canal, the infection is guaranteed to return. The only way to know if the initial treatment was effective, is to look into the ear canal with an otoscope.
Also, the most common cause of recurrent ear infections, even when they have been properly treated is allergies. Most allergens causing allergies in dogs are inhaled; dust mites, mold, and pollen. So, to answer your specific questions. The flakey skin you see is probably due to scratching and inflammation secondary to the ear infection. Any topical antibiotic ointment would probably be beneficial and certainly due no harm as long as it appears to be working. However, the bigger issue is the repeat infection. You need to have the ears rechecked. Be sure that the veterinarian uses an otoscope to visualize the ear drum. Ask him/her if the horizontal ear canal is clear. If not have him/her show you how to safely flush the ear canal. If flushing is needed to remove debris in the ear canal follow your veterinarians protocol for flushing and treating the infection. Then, be sure to have the ear rechecked at the end of the treatment period to be sure there is no longer any debris or inflammation in the ear canal. If deberis still remains your veterinarian may need to anesthetize your dog to flush the ear canal using a syringe and catheter to be sure to remove all debris. If there is any remaining inflammation, then the type of medication being used may need to be changed or a culture of the ears taken to see if there is resistant bacteria or yeast. Finally, if the infection and any debris has been documented to be cleared up, and the infection comes back, then it may be worthwhile to test for inhalant allergies. I know this is long winded, but it is important. I've seen too many dogs suffer needlessly because of not following through on proper care. Hope this helped
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No doctor patient relationship is formed by this communication. This advice is no substitute for a complete physical examination and appropriate diagnostics provided by a licensed veterinarian.
After seeing the results of less than adequate treatment result in extreme suffering in too many dogs, I cannot in good conscience advise other than to have her seen by a veterinarian.
The ear is a delicate organ, it is not amenable to home remedies.