your child seems to have Acute Gastrointestinal Infection
, in this condition patient may develop pain abdomen and loose watery motions, if your daughter is passing up to 5 motions a day you need not to worry, try to give her more liuids to avoid dehydration
. but as you have stated that you find some purple dots, it might be blood spots because of the damage of the mucousal layer of the intestine. any how its better to consult a pediatrician
near by you.
and as you said that she had also having severe nose bleed without clot and lasts for 11hrs,that condition is known as Epistaxis
. this is more common in children. was it first time? or was there any history of same condition if yes better to go for some hematological investigations like CBP,BT,CT, etc
take care care bye