You don't have short face 'syndrome'. You have what is sometimes called 'short chin'. But still it is a STRONG chin. Like sometimes you see that type of chin on a LIBERTY DOLLAR COIN. So, it has a positive connotation and within the norm of having a compact face.
The chin you have is sometimes referred to as 'short' because it is tilted upwards. But having that type of chin DOES NOT MEAN you have a 'short face' and most certainly NOT 'short face syndrome'. You could probably get away with just having a genio that tilts it downwards if you wanted your face to look a little longer.
If you wanted to go for surgery, most likely it would be double jaw and not only a BSSO. It would probably be CLOCKWISE rotation (which involves a cut to the maxilla) to orient clockwise which would set the soft tissue of the upper lip backwards in addition to tilting down the lower jaw along with the chin. With the tilt down via the clockwise rotation, the advancement of the mandible (via the BSSO) takes place over a more downward vector and provides elongation. Also, with the tilt down to the maxilla tends to mitigate the upper lip area sticking out too much. How much each is advanced would depend on your BITE because that needs to balanced with the extent of advancement. Possible you might not even need a genio along with it.
Illustration included (left side of it).