The posterior compartment contains the brainstem and the cerebellum. The brainstem is the connection between the brain and spinal cord, containing the origin of nerves involved in the control of breathing, blood pressure, eye movements, swallowing, etc. This connection occurs through the large hole, known as the foramen magnum, within the center of the posterior compartment. The cerebellum, lying behind the foramen magnum, is involved with coordination and balance. The roof of the skull base is composed of the brain itself and a thick sheet of tissue on which the brain rests, called the tentorium. Adding to the complexity of this region is the fact that each compartment of the skull base is at a different level. The anterior compartment is highest and the posterior compartment lowest, when a person is standing and looking forward.
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.