While it's good to get regular scopes when you have had colon cancer in your family, I would point out that your grandmother was in her 70's at the time she got hers. Old people are always more supceptible to cancer because of cell mutations that happen when your body is old and has been replacing its cells for a very long time--cancer is, normally, an old person's disease. If she had gotten the cancer when she was 40, that would put you at higher risk, because that means that something is going wrong with the genes too early in life. But, given that it's not appeared anywhere else in your family, and that your grandmother was already quite old, I would not worry that much. Like I said, it's the stuff that happens to younger people that you really have to be on guard for.
But definitely get the scope and set yoru mind at ease. From your descriptions of the blood, it definitely sounds like internal hemmroids, although you're still at more at risk for it being an IBD than cancer. Biggest likelihood, however, is IBS with hemmies. Two most common bowel complaints there are.