Welcome! - Could you confirm that you've read the Q&As?http://www.elevenplusexams.co.uk/appeals
(B11 in section B suggests a range of academic evidence.)
The focus should be on high academic ability rather than "qualities of perserverance, application and ability to work independently".
Unless you have reason to believe the school will be undersubscribed, you also need to give valid reasons for wanting a place - see section C of the Q&As.
In so far as there seem to be extenuating circumstances (let's hope the invigilator recorded what happened!), and the score achieved is quite close to what was required, I would have thought it's well worth a trying an appeal. Obviously the tougher the competition for the school in question, the harder it could be to win an appeal!