Another thought occurred to me -

I know your GP seems, at this point, to be unwilling to refer for phobia therapy. However, what about mentioning to her teacher that you are struggling to get therapy for her. Every school has an associated educational psychologist, and maybe she could give some pointers of a direction to go in, or steps towards a referral ? The educational psychologists are those who visit the SEN head every now and again, their remit is behaviour and learning issues (which they are often incredibly busy with of course), but if this is affecting your daughter's school experience and daily life....then....?