If you've got a microphone, you shouldn't be getting volume from your vocal chords - if you want louder, turn up the amplifier. Consider that the electric guitarist who's drowning you out is making an incredibly quiet sound, until his amp gets hold of it.
If your amplifier doesn't go loud enough, then either you need a more powerful PA, or everyone else needs to go quieter. When inexperienced people play in a rock configuration, there's often a tendency for "everything louder than everything else" - and often turning other things down is the answer (but it's difficult to convince everyone of this).
Make sure your microphone is one designed for live vocals. Typically that means a dynamic mic with a cardioid sensitivity pattern. That means that if you point it at your mouth, it will pick up your voice and not too much of the rest of the on-stage sound. This is a different set of requirements from a studio vocal mic, where normally other sounds are suppressed using other methods.
You shouldn't need to go super-close to the microphone. With a typical dynamic microphone, going closer will result in a more "boomy" sound. You can use that to artistic effect; many singers have a "voice" achieved by practically whispering into a very close mic - then as their voice gets louder, they back away from the microphone to get a more natural tone. The audience might perceive that as going from quiet to loud - but in fact the actual loudness if you measured it, is the same throughout.
It may not be that you're too quiet - it may be that there's not space for your voice in the arrangement. If your voice is occupying the same frequencies as the guitar part, then one will get lost in the other. For parts to stand out, they need to occupy their own slice of the frequency spectrum.