Tiny red pinpoint dots under the surface of the skin may be petechiae or vasculitis of smaller blood vessels.
Petechiae usually occur when platelet levels in the blood are low; they are small areas under the skin where capillaries begin bleeding (happens all the time) but cannot stop bleeding as soon as usual. The petechiae themselves are not dangerous but could be a sign of low platelets, which might be of concern depending on PLATELET COUNT.
Please get to a physician as soon as possible to let him/her check out the spots and possibly order a simple blood test (CBC) to check your platelet level.
If the spots are petechiae, they are more likely to occur in patches together, turn brown with time rather than stay red, and begin on the legs or feet.
If the spots are vasculitis, however, they will remain bright red for a longer period of time, may be somewhat raised, and will blanch out (fade briefly) with pressure.
From your description, the spots look like PETECHIAE and therefore you would need to get blood investigations to diagnose this.
Platelet count, Bleeding time, Clotting time, Partial thromboplastin time and INR tests would be needed.
Please discuss with your GP for appropriate referral.
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