@Bonaventurian,
That's a hemorrhoid. Fresh blood that's on the paper, but the stool (as we call it) is not itself bloody, suggests that the blood is coming from anus or very close to it. Hemorrhoids are just dilated veins that people get from bearing down (you can get them from constipation most commonly, but women often get them from laboring, and people can even get them from lifting weights).
Tylenol or ibuprofen is fine for pain relief if you need it. If it's itching and burning a lot I'd suggest getting some preparation H. And what you don't want is to keep pushing hard -- so if you're constipated you can try a sort of stool softener (I'd probably recommend just using something natural like prunes, or a fiber supplement like metamucil, but you could also try docusate sodium which is over the counter).
If bleeding and more bleeding continue, or you're getting lightheaded esp when you stand up, get ye to a doctor. A lot of things can bleed.