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.