Good points from herman (who is a medic, BTW).
The SATs & Head's recommendation are both fine, and if you have other good evidence (reports, school work, CATs, etc) then you should definitely go for the appeal. Your chances of success on 117 are statistically around 40%, but with strong evidence that will rise.
You need to do two things:
1. Ensure that you can explain this condition clearly and concisely to the panel, and provide evidence from the specialist.
2. As the new glasses had improved her sight by September, I am assuming that her schoolwork improved in September, if anything? If so, and as Herman says, you must be able to show how the condition would have directly affected her performance in the tests, as opposed to regular school work.