Hi Basil
Sorry to hear that your child was unwell - difficult to say it now but potentially would have been useful if this was at least discussed with the GP at the time.
Re appeals - these can't be done until your child is declined a place at the school ie after you put it on the CAF and not offered on March 1st. then you have to apply demonstrating high academic ability
I have to say however that appeals for non-qualification are extremely hard to win in the Birimingham area.
Have a look at the appeals FAQ
https://www.elevenplusexams.co.uk/appeals