Thank you for your query.
Do not panic.
She might have a nasal bleed.
Due to the cold
she is having the mucusy blood stained discharge.
Keep her nose dry by nasal decongestant nasal drops.
Apply some neosporin
ointment in both her nostrils for a few days.
Give her a mild antiallergic syrup to decrease the cold.
If you have any further queries you are free to consult me.
Hope this answers your query.
Wishing your child a speedy recovery.
Have a nice day.