I don't think it's cancer, but your tooth may be infected or have an abscess. That can be serious, not only because of the pain, but it can spread to the jaw and elsewhere. Left untreated long enough it can even be life-threatening. I don't mean to scare you, but it needs to be taken seriously.
Had your broken tooth been removed or at least capped early on, you would be in much better shape than you are now. The inside of a tooth is much softer and more porous than the outside. You can't clean it well enough to prevent infection.
I know dental work is expensive, but there are lower-cost options. You could go to the local dental college, for example. Or you could go to a dentist that will work out a payment plan.
Get to a dentist as soon as you can (like in the next week or sooner). In the mean time, try a warm salt-water rinse to soothe the tooth and over-the-counter pain relievers. The sooner you get this treated, the better.
