I agree with chantal21, you have to take it for more than one day in order for it to be effective. But if your as bad off as you described, I would call my primary care Dr. If you have a severe sore throat, you could have strep, which is contagious. And if you've had it that long and no relief, it could turn into phnemonia. Call your Dr back.
If you have some sort of infection you need to get to the doctor so they can treat it. I would definitely see what's going on. The blood could be irritation from coughing. When
i had bad m/s, I use to strain so hard when throwing up that blood would actually come up, not a lot, but enough. My throat was so irritated. If your doc told you take Robitussin, you may have to try it for more than a day. It needs to be in your system to work. Once you do that and it still hasn't gotten any better get to the doc to be checked out. You can also try honey with lemon to soothe your throat as well.