It seems from the history that your 12 year old son and 10 year old daughter had injuries following a fall. The symptoms of your 12 year old daughter seems to be benign but she requires evaluation to find out the cause for nose bleeding and treatment accordingly.
The symptoms in 10 year old daughter is having dizziness
, headache, nausea
... These symptoms indicate concussion head injury
and hence require evaluation and treatment accordingly. Hence she requires evaluation at the earliest.