So you suspect you may have a bad air conditioning compressor because you just charged your system fully with Freon and you still got warm air out the vents.
Quick and easy way to get a sometimes definitive diagnosis on a bad compressor coil & clutch assembly is to turn your car on, turn the AC on, open your hood and put a long metal object (pry bar, screw driver, etc) near the compressor pulley. If the metal sticks to the pulley (be careful you don’t get it jammed in anything) and you can see that the clutch is still not engaged and spinning than it’s time for a new compressor. This test is not always definitive because you could still have a bad compressor if there is no magnetic pull, but it’s a quick test that can save you a lot of other testing steps.
This test is meant for someone who has a decent understanding of how most automotive AC systems work.