My 2 year old granddaughter has been ill for 9 days high temp Drs can't give her anything say its a virus ?

We are really worried she goes very pale her lips go blue and she's like a rag doll and then her temperature shoots straight back up to 40 once the calpol has wore off she's ok for around 4 hours we've taken her to the GP and the out of hours surgery I'm worried it could be more sinister should we just take her to the hospital am considering going private