This puffiness is most likely to be due to a hematoma in this ear flap. Hematomas are collections of blood. They are common in ears because there doesn't seem to be anything in the ear to generate enough pressure to stop bleeding until the ear swells enough with blood. Ear infections, ear mites, fly bite irritation, mosquito bites, allergies and immune mediated diseases have all been implicated as underlying causes for this problem. Anything that causes the dog to flap its ears can make this happen and it appears to occur spontaneously in a number of dogs.
Activated charcoal can act as an adsorbent (kind of a "chemical sponge") to bind toxins in the gut. If you use a preparation that is safe for people and use a smaller dose, it should be harmless.
If the problem was an insect sting, I doubt that there are any toxins in the gut that the charcoal would help with.
So many times we are unable to determine the source of the allergen.
Kenalog is a long-acting corticosteroid (cortisone) injection that stays in the body for weeks, where the dexamethasone lasts only a couple of days.
Antihistamines like benadryl are often helpful for something like an insect sting, even though most dogs don't get much relief from them in regard to allergic itching.