My unit is blowing cool air but my fan on the outside unit is not turning

If the compressor is running but the fan is not, the compressor will most likely over heat and shut down on internal overload. It will repeat this over and over again which can be extremely hard on the compressor. I would get the fan issue fixed asap. Make sure to check the capacitor first, as it may be as simple as that. IF cap is good, you most likely will need a new fan motor. Good luck.