"I flushed the cooling system, sorta"= " I did not really flush the cooling system "

The block drain plug is low on the front passengers side of the engine...

The block core ( freeze plugs ) are in a line on each side of the block . They are about an inch and half in diameter. One of the will probably have a block heater plugged into it... typically the back one . Get new Brass plugs before you start, then take them out and flush with as hard a stream of water you can manage until the water is clear coming out of all the orifices..