I sing in the shower all the time! My boyfriend is going to school to become a professional singer, and he's been trying to get me to sing out in public more often. The main struggle for me is that I have to thicken my vocal cords, but that'll come in time!
I think the biggest fear of people singing in public is that we're afraid of sounding bad. But all it takes is practice, practice, practice! I've yet to hear anyone who is bad at singing, just inexperienced.