with having a well recommended BMW focused shop diagnose the problem. I do almost all of my own work but I leave other than the basic troubleshooting to see if it is something simple to an experienced air conditioning tech.
You can check the aux fan. If the fan has failed or isn't getting power the air conditioning won't work. When the air conditioning is on the aux fan should be running.
You can check the air-conditioning related fuses.
If this is your first BMW you may not be aware that the dial on the dash that in one direction shows a red dot and the other a blue one needs to be turned to blue and the snowflake button activates the air conditioning.
You can check if the compressor has power. The clutch on the front of the compressor should turn when the air conditioning is on.
Pressurizing the system beyond the recommended pressure for any reason is dangerous. Recharging the system without reading both the high and low pressure sides is too easy to overfill the system, causing damage-can seize the compressor. And the process of evacuating and refilling the system includes a vacuum and adding both refrigerant oil and refrigerant.