Tiny red pin prick dots on the skin are most likely petechiae. Petechiae are caused by broken capillaries which result in a small amount of blood depositing in the skin. Most often, petechiae are benign findings but sometimes they can signify an underlying medical condition such as low platelets, anemia, bleeding disorder, or autoimmune disease.
The best evaluation for petechiae is with a physical exam and blood test to evaluate the platelet count.