Uncle,
The reason for the shadow is that the camera's flash bulb is not in precisely line with the camera lens, it's offset an inch or so to one side. So the flash, which acts just like an intense spotlight, illuminates the scene from a slightly different angle compared to that seen by the camera lens, the result being the shadow that you describe.
Another thing that might help, instead or as well as those suggested, is to rotate the camera to somewhere halfway between vertical and horizontal, so that built-in flash is vertically directly 'above' the lens rather than to the side. There will still be a shadow, but it may be less noticeable, as it's a downward shadow rather than a sideways one, so it only shows below the hair and ears in a typical portrait type shot. Of course, you must rotate the image back again to level it out for printing.
- 7LM