Welcome to HealingWell!
Yes, I do believe your grandmother's cancer is part of your family history. But, it doesn't mean you're going to get it too. The odds are higher for you when you have an immediate family member with cancer. Also, I read at about.com that most colon cancer appears in people with no family history of it. I think as long as you're getting scoped regularly that's the best you can do.
I wouldn't worry too much about it with your current symptoms. Everything you're describing could be IBS and/or hemorrhoids and fissures. Have you tried adding fiber to your diet? It might help with the straining and irritation you get. Stool softeners can also help with that.
When is your scope? It wouldn't be good for you to stress over this for too much longer.