Helllo Kthrone. This sounds like a petechial rash
. This is a rash caused by small bleeds in superficial capillaries close to the surface of the skin. They often appear when increased pressure from actions such as coughing or vomiting
causes the tiny capillaries to burst or leak a little, or by friction like rubbing of the eyes.
Given that there is a family history of allergies, your daughter might have an allergic irritation causing her to rub her eyes to the point of aggravating these capillaries and causing this rash.
As unpleasant as it sounds it isn't anything to panic about. I would suggest having her platelet count
checked, just to ensure she doesn't have an underlying bleeding problem. Then start to make a note of the environment (eg dust, exposure to certain flowers or pollen, animal fur etc), food eaten and so on, on the days the rash develops. This may help you narrow down potential allergic triggers, she could then be tested for IgE's (allergic markers) to specific triggers.