This is what the bible states. The beast out of the sea has a wound to the head and the people are amazed that he is still alive. It refers to this wound as being caused by the sword - which does not mean it is caused by a sword but rather that it was received in a war or during war time.

When the bible speaks of a sword it typically means war.

The false prophet follows him and makes an image of the beast from the sea. It is the false prophet who breathes life into the image, in the same way God breathed life into man and then makes people worship the beast and the image of the beast.

That is what it states about head wounds.