Could this little black skin bump be a tumor?

Skin cancer?: If it is new, and grows fast, and the border is very irregular, the surface color can be not uniform (black-red-black, or just dark black..), then it most probably is skin cancer.

It could...: ...But it could be other things, such as a small pool of blood called a "venous lake." remember that not all tumors are dangerous; most are not, actually. But someone (preferably a dermatologist) needs to look at it to give you a definite answer.