I sprained my metacarpal finger about 3 weeks ago and it's still hurts and is bruised, now other metacarpals on the same hand hurt and r bruised.

You could have break. In one or more metacarpal check it and take x-ray to be sure.
A stiff and swollen. Finger can easily affect the motion in the adjacent fingers. Fingers are linked to some extent by tendinous connections, nerve supply and shared circulation origins, thus what happen to one foinger can affec thte way others move, feel refer pain and swell. Its important to make user that your "sprain" is nothing more and that your joint can be passivley mobilized safely .