From your
description, these sound like petechiae, which are broken capillaries
forming red dots that don't blanche or go white when you press on them. They
can form because of trauma, low clotting factors such as platelets, or in
genetic inherited blood disorders.
Do any
other family members have these kind of skin dots? Have you had a blood
count done at any time to determine that your cell counts are normal? Do you
bleed easily if cut?
You
certainly can come in to show a health care provider what it looks like so
we can be more specific about the potential causes.