Missing info: The more info you provide, like (the kids age/duration of problem/past treatments/etc.) the more likely we can focus on a reliable answer. The nasal membranes contain many fragile capillaries that bleed easily from the trauma of picking/rubbing the face in a pillow/etc. The bluish haze of the lower lids suggest nasal allergies. This is common. Nasal saline washout usually helps.
Answered 3/12/2020
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