A/C started blowing cool instead of cold

Adding any refrigerant without checking the actual amount in the system is not a good idea. The groaning may have been the AC compressor shutting down from high pressure from an overcharged system.
The likely issue is a bad blend door actuator, it moves to change the door that directs air through either the heater core (default position) or through the AC evaporator core. The problem is that to get to that actuator requires the dash be removed to access it on the back side of the HVAC box.

What I would do is take it to a shop that has a factory level scan tool and have them test the blend door and the control head. That would verify which is the problem. Then have the AC system recovered and see if the compressor is still operational with the correct charge in it.