Impetigo
A contagious bacterial infection that is often easily passed between children. Impetigo is characterized by red sores that open, ooze fluid, and then form a crust.

Vasculitis
A disease characterized by inflammation of the blood vessels. Vasculitis causes red spots to appear on the skin and may be related to autoimmune diseases or infections.

Hemangiomas
These are birthmarks resulting from abnormal growth of blood vessels. Occasional medical intervention may be necessary, but they are usually harmless.

In conclusion, the appearance of red dots on the skin does not necessarily mean that you should worry. That said, it is important to consult a doctor if:

Red spots are accompanied by fever, pain, or other discomfort.
The spots increase rapidly in size, number, or intensity.
These spots are accompanied by other symptoms such as fatigue, weakness, or dizziness.