Can Taking one baby aspirin daily thin the blood too much?

I already have thin blood, but have been prescribed one baby aspirin daily to keep my blood thin, but I have three blood splotches showing up on my one forearm daily, I have continued to take the aspirin - for my heart,the doctor says. Is this safe- to take a baby aspirin daily? Please help: I think that it is depleting my strength. thank you. efb2010@yahoo.com