I'm sorry to hear about your injury! We know how painful that can be. My fiance injured his shoulder last fall, and the pain came on about a week after a night of bowling. The pain got so bad it almost brought him to his knees, but with no health insurance at the time, he was unable to see a doctor. We diagnosed the injury as best we could and did the same thing a doctor would have told us to do: Rest, ice and take OTC pain relievers. He wore a sling every day for the next two months, especially while walking, to keep the arm from hanging. He iced it at night and relied on ibuprofen or naproxen sodium for inflamation and pain relief.
It's important to keep using the sling as your shoulder starts to feel better, to reduce the risk of another tear. My fiance stopped using the sling too soon and found himself in a considerable amount of pain within days. He also found that his sleeping position aggravated the injury - if you're a side sleeper, both sides can cause problems either by pushing or pulling your arm too far. Your back or stomach would be the best sleeping positions while your shoulder heals. You may also find some exercises to strengthen the muscles around your shoulder, just be sure to keep your arm close to your body at a 45 degree angle.
I'm certainly not a doctor, just a copy editor in favor of taking the path of least destruction when treating injury and illness. I myself experienced the worst pain of my life with a herniated disc in my lower back. It was bad enough I lost all use of my right leg for a few weeks, but sure enough, it healed with time as these things do. Today, I walk just fine, and my fiance is sling-free and enjoys full use of his arm with only small twinges of pain here and there. All it takes is a little patience and a lot of time.