Hello~ This sounds very similar to petechiae which is a small red or purple spot on the skin caused by a minor bleed from broken capillary blood vessels. One thing that can help the capillaries is the citrus bio-flavonoid vitamin, a relative of Vitamin C. Taken together strengthens those capillaries and the bruising/under-skin bleeding should stop.
If they don't clear up or you get more, then I suggest seeing your doctor for some blood work to rule out any serious issues that could be causing the problem.
Sounds like petechiae (a small red or purple spot on the skin caused by a minor bleed from broken capillary blood vessels). Causes are numerous but include injury, allergic reaction, blood infections, autoimmune disorders, medication side effects.