"Children with exceptional medical, social, or psychological needs, where it is agreed by the local authority and headteacher that these can be best addressed at the school"
Ah, i suspect this may be where you have come unstuck. Did you consult with the head and LA before you applied to ensure that they agree that this school is the only one locally that can meet your needs? Or did you just supply your own medical documentation?
Obviously, now the EHCP has been granted, you are in a much stronger position (does it actually name this school though?), but at the time you didn't have it officially agreed that the medical requirements could only be met by this school.
If the EHCP names the school now, then you would have a reasonable case at appeal I would suggest (as you could argue that the LA made a mistake, knowing that the EHCP which names the school would be complete soon, in not putting your DD in the priority category).
If the EHCP doesn't name the specific school, you are on shakier ground, because the official line from the LA will almost certainly be that all schools in the LA are equally good and can cope with special needs.