You can ask your doctor to confirm this, but my understanding is that one shot of prednisone will not have mental effects. It is sustained use of steroids that can lead to mental reactions. However, there is a good chance it can raise your blood sugars so pay extra attention to your testing and treating of your diabetes.
Short term low doses of Prednisone is not harmful unless you already suffer from emotional instability. If your eyesight gets blurry and/or you feel emotionally distressed while taking Prednisone contact your doctor immediately.