You probably should call the doctor. The odds are it's nothing serious and they will be able to reassure you. They won't dismiss you. They might tell you there's nothing to worry about and recommend a cream, but that would be good news. 

It could be a whole load of things, the most likely are probably hemorrhoids or a fissure, because of the constipation, but it's worth getting checked out because it could be a lot of other things too, such as ulcerative colitis or Crohn's disease or even something like divercular disease or a polyp (though I'd say the latter two would be unlikely at your age).

Cancer would be very uncommon at your age. I had rectal bleeding (not as much as that) combined with some other symptoms over the summer, at the age of 40, and the consultant said that he'd be worried about cancer if my mother came in with those symptoms, but at my age, it was possible but highly unlikely and I would be "the most unlucky person in the world" if it turned out to be that. Which it didn't. It was hemorrhoids. At your age, it would probably be even less likely, especially as it sounds like you don't have any other red flag symptoms (like weight loss, abdominal pain, change in bowel habits...), but it is still worth finding out what it is. On the off-chance it is anything serious (Crohn's, ulcerative colitis, a polyp...), the sooner you get treated the better and if it's not, then the sooner you know for sure, the better.

People your age can definitely experience things like that. Yeah, cancer, polyps and divercular disease (which I can't spell) aren't common at your age, but ulcerative colitis, Crohn's, hemorrhoids, fissures, infections, gastritis, can all happen at young ages. And that's just what I know of. I'm no expert.

I don't think you should be too worried, but maybe call the doctor and ask their advice and maybe try and change your diet a little (though I'm a hypocrite for suggesting that since I am not even following the diet that was suggested by the consultant after hemorrhoids were confirmed).