My problem comes when I attempt to send the data to Processing and create a .csv file with the data. Arduino and Processing are both attempting to use COM3, and of course they can't at the same time.
Sure they can, as long as Processing is the only application on the PC that is trying to use that port.
If you mean that Processing and the Serial Monitor can't both use COM3 at the same time, you are correct. So, close the Serial Monitor.