Get a medical examin: Red dots like you have described can be caused by a number of possible reasons. Leukemia is low on the list. But if you want to be sure you need to have a check up by your doctor who can do a blood count(cbc diff and platelet count) to check your blood numbers especially platelet count , which if it is low, can cause small red spots over the skin of your legs and arms... Called petechiae.
Answered 7/10/2018
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