Maybe you could record yourself on your phone or any other device, just for the sake of getting to listen to your own voice. But singing isn't really about being good or bad, it's about enjoying the moment even though your best friend's ears hurt (been there, done that). And I'm sure you'll get over being so shy one day, and when you do, you can just ask people to be honest and tell you what's their opinion on your singing. And if it's negative it doesn't mean you should ever stop singing or anything like that.
:)

Singing really isn't about being good or bad, it's about having good technique. Actually, most pop artists nowadays are terrible singers! They are just so autotuned that nobody can tell. (Think taylor swift in concert vs on a CD) If you really want to learn to sing well, try to see if you can get lessons from a friend in choir, or join your high school or middle school choir. I used to think I sucked even though everyone else told me I sounded fantastic. Then I joined choir my freshman year because my friend talked me into it. I started getting solo after solo and it made me realize that hey, I actually might be really good! :) If you want to know good technique to sound great, I can help you out with that. I've had 6 years of choir experience and three years with experience doing musicals. :) And yeah, I know how to sing pop music too. :P So I guess bottom line is, even if you may not sound too good now, vocal training will make you sound fantastic. :)

Sing in the shower!