The compressor shouldn't have anything to do with how cold the air is coming out of the vents. like said before did you install it yourself or did you have it done professionally? A compressor is basically just a pump that moves the freon through the system. If you had it done i the past few hours it could be it just hasn't had time to cool the house down everything in your home holds heat and will take a few hours if not over night to get everything cooled off. If it's been over 24 hrs id say its probably a problem with the charge. Also make sure all your filters and coils are clean. If you walk outside and look at the unit it should have hot air coming off the top fan and the big copper line should be beer can cold if not its probably the charge like i said b4.
Put a thermometer in the center vent turn your a/c on high. Drive down the road so you will have adequate air flow over the condenser. The temp should be around 38 to 40 degrees at the center vent. If it's warmer than 40 it won't keep up with the heat. If it's not cold enough it's probably a low charge. Two causes for low charge 1. it wasn't charged properly in the first place 2. it's leaking.
I did it myself , changed out compressor , accumulator , and charged it . It was fluctuating for a min on first startup but I just took it for a ride and it smoothed out and now its getting and staying cold. My ol 96 bronco