Yes, blood in urine is normal for a few days, particularly the first few cc's as you start peeing in my experience. You may get bits of clots too.
Blood in semen is even more common, and can go on for 3-6 weeks, and can look very dramatic (you would think it was pure blood). After a few days, it changes from bright red to brown, and then gradually gets fainter.
By the way, as the charity which did my original PSA test said, the most common symptom of PC is...
Which is of course indistinguishable from no PC until you've been fully diagnosed.
At the stage when the symptoms are nothing, it's at its most curable.
I had exactly the same emotional feelings, as did many others here.