Ice should be used only for pain. It actually delays the recovery process the body naturally performs. Soreness should be treated through using the arm again. The goal is to get blood flow back through the body and arm (the new blood kicks the crap out). Rhythmic stabilization, tubing, plyoball throws and foam rolling can all help this process.
Your everyday life affects recovery as well. How you hydrate, eat and sleep all play a roll. A rule of thumb I use is drink an 8 oz. glass of water/hour. Try to get at least 8 hours of sleep (I know we’re all busy, but try when you can), and eat as much raw food as possible as it’s the best for energy and the health of ligaments and tendons.