It's not your voice or your laptop. It's probably your ears and practice. The way your voice sounds to you, resonating in your head sounds different than from an audience's point of view. You need practice singing and recording these songs and listen to your dynamics, pitch and tone. As you hear it back, you'll find in one segment your always sharp, so make the adjustment and try it again. Once you get that move on to your next problem and practice and fix that. Repeat this until this song sounds the way you think it should sound. No out of control volume jumps or pitchy notes. The next song you sing will be easier and so on.
On a side note, using a cheap dynamic microphone through a crappy sound card, mic pre amp and crappy computer will be a poor representation of what you really sound like. Having decent equipment isn't necessary but it certainly helps and encourages.