Cessna 402C Captain reported aircraft wheel vibrations during landing; aircraft veering on the runway and aircraft stopped on the runway.

Narrative

When the main wheels touched down; the nose abruptly dropped despite the back pressure I held on the yoke. The aircraft rolled down approximately 1;000 feet before I started to feel the right wheel vibrate and the nose start to shimmy progressively worse. When the plane started to turn towards the right I applied brakes to prevent the aircraft from veering off the runway. When I came to a complete stop; I attempted to taxi the aircraft with differential thrust but the aircraft would not budge. I made a call on CTAF and to ZZZ Approach before shutting down the engines to let airport operations staff pick up the passengers.Cause: The right brake may have still been locked up on impact. Possible runway FOD or mechanical issue as well.