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Leukemia is blood cancer, and it does not show petechiae. Leukemia comes with severe weakness and mostly from birth only. It is hereditary only, so do not worry. Your own thoughts make you anxious, so I would suggest you not to think about anything because you do not have any severe symptoms.
Take a blood test, so it will give a hint and rule out your leukemia as well. In leukemia, there is increased blood cell in huge amounts. I have seen many patients with leukemia in my life, and none of them had such petechiae.
I would suggest you take the treatment I suggested for five days and let me know along with the below details:
1) Is there a history of leukemia in your family?
2) What makes you think that it is leukemia?
3) Did you lose plenty of weight in the past years?
4) Do you have severe weakness or bone pain?