There's a good chance that if you're fairly new at playing the guitar, singing or both, that you're afraid to play songs in front of people; whether at an open mic night or even just in front of your friends.
This comes from an irrational fear of rejection that you should squash immediately. That kind of social fear is left over from when we were a primitive species living in small tribes where you pretty much only knew people in your tribe and maybe some from neighboring tribes. If your ancestors got socially rejected in that setting, it could mean they wouldn't find a mate or they would get booted from their tribe all together. You on the other hand, have probably met more people in school last year or at your last job than your ancestors met throughout their entire lives living in these tribes. Unfortunately for us, our species spent the vast majority of its existence living this way and we haven't outgrown that fear yet.
Let's face it, that kind of social fear is useless to us now, especially as it applies to playing music in front of an audience. If you play at an open mic night, fumble through a few songs or even completely bomb, chances are good that you aren't going to see any of those people ever again. If by some freak chance you ran into one of them a week later, they probably wouldn't remember you or they'd admire you for getting up there and trying. We're all human and we all have those fears, people know it takes guts just to get up there.
Usually when I feel those butterflies in my stomach and I'm nervous about something social, whether it be talking to someone I don't know, saying something important to someone or playing on stage, I know that that's exactly the thing I should be doing. It's like telling someone you love them for the first time, you're putting yourself out there and you're not sure what kind of reaction you'll get. It's scary but it's necessary because it'll expand your comfort zone and help you grow as a person. So play in public, get up there at open mic night, sing a song at a karaoke bar or bust out the guitar (or ukulele) when you're hanging out with your friends. Afterwards, you'll be glad you did.