Hi ,It is a good news that her platelets have increased without being treated. An 8 Yr old kid can have nose bleeds for several reasons.It is a problem only if it the bleeding is heavy and doesn't stop even after 5 minutes.In case of kids ,if it is ITP ,they will recover after some time ,naturally without any treatment.Since her platelet count is 47 K ,I think it is quite safe (not alarming).You can proceed with your first doctor .
My son is also 8 yrs old.He is having ITP since he was 2 yrs old.