Are we at the beginning of a Heinrich Event?
Definitely not.

A Heinrich event requires massive ice sheets to grow and then collapse in the Northern hemisphere. The large outflow of icebergs that would result form such collapse would deliver fresh water and debris to the North Atlantic, which is what constitutes a Heinrich event. These events are detected by existence of deposits of ice rafted debris and dropstones in the sea floor.



Example of a dropstone carried by an iceberg, dropped on the sea floor, and then embedded in sea floor sediments (image taken from snowballearth.com)

Current ice masses in the Northern hemisphere are tiny compared with those that generated all recorded Heinrich events.

Something similar could happen now further south if East Antarctica collapses. However the circulation pattern in the Antarctic ocean limit significantly the distance that icebergs can travel.