Thanks for your message, and I'm so sorry to hear about your circumstances.
I'm afraid extenuating circumstances form no part of the admission arrangements. If two children tie for a place, then only the published admission rules for the school can be used to determine who gets the place.
Extenuating circumstances can only be considered at appeal - and you cannot submit an appeal until after 3rd March (when your application is formally refused). Most appeals will be heard in the summer term.
In the lead up to the 11+ it would have been possible to notify the relevant authority of any extenuating circumstances, but this would have been to get something 'on the record' at that point in time - with a view to an appeal if not allocated a place. Notifying the authority now, after the results have been published, wouldn't carry any weight.
We give advice about appeals in the Q&As. For example:http://www.elevenplusexams.co.uk/appeal ... cation#b11http://www.elevenplusexams.co.uk/appeal ... -school#c2