When they mentioned "short latch" did they also say that your LO could be tongue-tied?
I would check with your Ped rather than rely on your LC. LC *can* be nurses, but many times they are not. Plus, I saw three LC's during our hospital stay and not one of them caught it.
As far as intervention, they may decide it will lengthen on it own, but other times they may decide it requires intervention and choose to "clip" it. It is a 2 second procedure in an ENT's office and they can do it while you are holding your LO.
Babies that are tongue-tied can not only have issues with latching that can cause the mother pain when nursing, but it can also cause other issues, as well. Just as the tongue cannot extend forward enough to latch properly, it also can't sufficiently block the airway to prevent air from entering the stomach and causing gas. There is debate about whether or not it can also cause speech issues once they begin talking.