Nerve hit during Botox
There are a lot of sensory nerves in the face and yes, what you are describing, a feeling like an electrical pulse from the site up into your head, is exactly what happens when a nerve is affected. I have never seen this be permanent, but I have seen it take up to about 6 months to resolve fully.
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Nerve hit during Botox injection
Sometimes when Botox (or any other injectable product) is used on the face, it is possible that a sensory nerve can be hit during the injection. This does normally cause a electrical type sensation that travels along the course of the nerve. When this occurs on the forehead, the sensation usually heads towards the top of the head. There should be no long term issue when this happens although there can be a strange feeling when the area is touched for a period of time. In my experience, this sensation has always gone away but the time for it to resolve can vary.