Have you had a CBC w/ DIFF? If you have leukemia, that will most likely be very irregular. Have you talked to your doctor about the dots? From what you say, it might be petechiae, but I am no medical expert, so if you have not asked your doctor already, please do. Some people just naturally get them more than others - I tend to get a few every once in a while for no explainable reason - and most things can be explained by something other than leukemia.
Hope you get better soon!