You should wrap a cold pack or some ice in a towel and place that on the sore area of your arm. But for no longer then 20 minutes.
Rest for a while, making sure to raise the injured area above the 'heart level
Massage the area a few minutes every hour. This is supposed decrease swelling and increase blood flow.
Then you should put a hot compress on the injured area, but only if the swelling has gone down, if not then wait. If it has then dont do this for more then 25 minutes at a time.
Compress the injury with an elastic bandage/gauze. But dont wrap it so tight that you cut off circulation. If your arm starts to turn blue, then you have cut off the circulation.
Then after a couple of days, gradually start moving your arm around and doing small stretches and such.
If swelling doesn't go away in four days, you should have yourself checked out by a doctor.