Monitor speakers generally run from the PA system wherever you're playing. You either mike your amp or use a direct out for the PA. Monitor speakers may be floor monitors or "hot-spot" monitors that mount on a mike stand. With monitors, you are using the power of the PA amp (usually a lot more than your guitar amp) and the ability to point the monitor speakers at your ears.
You may just need a more powerful amp to keep up, but try this. Put your amp on a stand or a folding chair (if it's not too big), tilt the amp back to point towards your head. Move closer to the amp. All of these will help you hear yourself better.