Lying on your left side does give the best blood flow to the uterus and to your kidneys, so it's good to hang out there, but there's certainly no problem with the right side. Left side is also best if your blood pressure is high. Use a pillow as a wedge if you find yourself on your back a lot. With the doctor's permission, engaging in sexual activity can hurry up labor a bit. Also, gentle stimulation of one nipple can bring on mild contractions and gently hasten things.
Some people believe acupuncture can also bring on labor.
Try drinking MORE water, believe it or not. It will rev up your kidneys to pee out even more than got put in. Of course, the side effect is that you'll be up and down all night to go the bathroom. Also, lie on your left side as much as possible. This encourages more efficient kidney function, which pulls out some of that water.