I haven't been to an appeal (yet!!)
If you can get this diagnosed from the doctor then yes, mention it. Otherwise allergy tests are not conclusive...And certainly wouldn't stand up in an 11+ appeal.
We are all allergic to something... I'm allergic to 11+ tests ..
Honestly my brother is an allergy tester and If I went by what he has tested me for and confirmed I should avoid,,, I wouldn't be able to eat or be near anything...
You've got the Heads support (which is a big +) . Level 5's for core subjects,,, 3 Marks below the pass mark.
I really don't think you can do any more... It's just convincing them your daugther would be better off in a Grammar School and this is where she should be.
I wish you Good Luck,
p.s Any idea how many other kids in the school did not make the cut ?? My friends boy was the only one who failed his 11+ last year in a group of 20 and surprise surprise all effort was made to get this boy through appeal by the school which he did.