I don’t know of any API method to achieve this, but it can be done:
Get the parent
Walk through it’s children to find the index of current
Get the index below or above and you’re done
C# Example to get the next child (or null if it doesn’t exist)
Transform GetNext()
{
var myself=transform;
var parent=transform.parent;
var childCount=parent.childCount;
for (int i=0;i<childCount-1;i++) { // skip the last, as it doesn't have a successor
if (parent.GetChild(i)==myself)
return parent.GetChild(i+1);
}
return null;
}