Everyone has had them. A hard bout of coughing or vomiting can cause facial petechiae, especially around the eyes. These mean nothing.
Newborns often have facial petechiae from the tight squeeze through the cervix.
Thus petechiae are fairly common and in general of no concern. Petechiae that appear during illness, especially illness with fever, can be a different story. If present, they could be be the heralds of very dangerous sepsis , even in a child who does not look all that ill.