For instance, I totally can't sing karaoke but I'm a trained chorister and I can sing solo parts well just as long as I don't have to see/hold/sing directly into a mike.
You might be having "mike" fright. Try singing with the mike held a bit lower at first until you become accustomed to the sound of your amplified voice. Then you can gradually bring the mike closer to your mouth. Practice this at home before you sing out.