Today, when I tried to land in the new 3D Jamaica airport, in the short final, the aircraft start heading to the left and then to the right without no sense. It was weird.
Then, when 50 feet or so above the runway 9 in Punta Cana new 3D airport, the aircraft start to heading to the left and then to the right. In this last case, the aircraft look like it was to stall but, as near the runway, that was a very bad land.
What was your kt speed? Sometimes when the speed is too low, the autopilot starts swinging the wings of the aircraft to maintain a rate of climb or descent so that a stall is prevented
Depending on the situation and weight of the aircraft, 135 can be just barely enough. Usually 130-150kt is good for the 737. If it’s not speed, it could be your flight plan, and you may have kept the autopilot connected to a waypoint that forces the plane to turn.
By this did you mean it is mostly banking from side to side?
That is a possible clue. If the amount of cross wind was changing, the autopilot should be trying to compensate to keep your direction aligned with the course.
And if your speed had less safety margin, there might be some movement back and forth as the autopilot tries to control.
This is just one guess without seeing a video replay.