You only get one voice.
While it can take a fair amount of abuse, you still need to respect your instrument. You should always strive for a clean sound before you distort. Getting emotion in your voice comes from release and freedom, which is ultimately technique. There's a way to do it that is more like a gentle rubbing of the cords with the right amount of compression and placement.
Singing, in whatever style you choose (pop/rock, etc) is always about shape, not force. A low diaphragmatic breath is only one part of the equation. Are you warming up? Most likely you have not been singing on an open throat or have developed your head voice, which will allow you to sing higher. I would be happy to help you rehabilitate your voice, but we will first focus on a clean, clear tone. Before you break any of the rules you have to understand what they are.