akt416any physio will tell you if its sore, move it, work it, then ice it. if youre not moving it at all then it wont swell (i.e. no sense icing it) but if its the joint youre worried about you should definatly be doing some light exercise with it to keep blood flowing through the area. then yes, ice it after
Why would you ice it, what does it accomplish? You say you should move around to get the blood flowing, and then apply ice, which reduces blood flow. That's counter intuitive, and your body increases the blood flow around the injured area on its own anyways. Moving it is good though.
Ice interferes with the inflammation process, which is necessary to properly heal an injury. You can elevate and use compression to reduce swelling, no reason to use ice. Every physio recommends icing? Certainly not any of the ones i have met. There isn't even any good clinical evidence showing that icing is beneficial.