Hi Zeinab - welcome back!
Did the school have any particular requirements such as notifying them without delay if your child was not fit to take the test?
Have phoned up the schools who have said in order to appeal you need to place it on the CAF.
That is certainly the convention.
There is a possible legal argument to be had that any
decision (such as the determination of non-eligibility for grammar school) triggers the right of appeal.
[AS v Buckinghamshire County Council  UKUT 407 (AAC).]
Not much point considering this, though, unless you're prepared to go to court!
Only your particular appeal panel could tell you what view they take of not having reached stage 2 of the entry test procedure. They are certainly obliged to give proper consideration to your case, but I would have thought it inevitable that, the greater the competition for places, the more difficult it is likely to be to win an appeal. This is because, even if you have an excellent case, the panel is required to consider whether the school could cope with the total number of (potentially) successful appeals. If they decide the school could not cope, they are obliged to move away from “each case is considered purely on its own merits,” and they have to start comparing cases. They prioritise all the cases, and decide which of them to allow (up to the point where they judge the prejudice to the school has become too great).