I like to sing, but I'm afraid?

I love to sing. It makes me feel good. I don't sing to any of the music I WRITE, but I sing to my favorite bands/songs. But I am terrified of doing it. I have no idea whether I'm good or bad, though I ume I'm pretty bad. I'm a 16 year old guy, so trying to get a high octave range can be a challenge sometimes. Recently, I got "Green Day: Rock Band" for the Xbox 360 because their stuff from the 90's is my favorite music ever, and I love playing Rock Band drums (and YES I play both real drums and guitar, I swear to God). But I decided recently to get a microphone for the game so I could sing. I've only played a few songs so far because of my nerves. I get so afraid of someone hearing my voice, that unless every door in my house is locked, including the one to my room, and unless the volume on my T.V. is up pretty high, I won't do it. I know it's ridiculous, but it's terrifying for me, and I've had experiences where people have walked in when I'm singing. This has become kind of a ridiculous phobia for me, and I think a lot of it has to do with the fact that I have both anxiety and depression. But now more than ever, I REALLY want to come up with the courage to do it because I've been writing music lately, as well as recording. So far, I've recorded the guitar and drums to this song, and so I still need b and vocals. The vocals I think will be primarily stuff (Cannibal Corpse style), which I think I'm DECENT at, but that makes me even more nervous because it's just so different. Any tips to get over this?