Baseball pitchers were one of the first to put large ice packs over their entire pitching arm and ipsilateral shoulder.
Muscles become inflamed with overuse. The US Women’s Beach Volleyball teams climb into an ice bath after play.
RICE--Rest, Ice, Compression, and Elevation is the intervention used for newly sprained joints like the ankle. Ice does wonders for pain caused by inflammation...for about 20 minutes. It numbs the area, constricts the capillaries so that they don’t “weep” plasma into area--the swelling we see with injuries.

I imagine that LBJ (King James) overuses every muscle in his body. Ice feels great. Anyone with chronic pain, e.g. tension headaches can relate that putting bags of frozen peas encased in wet towels to back of neck and over the forehead can relieve pain completely.

Cold interrupts the inflammatory-increased pain--more inflammation cycle.

I have such severe degenerative joint disease that getting into a bath tub with ~50# of ice is the only way to stop the deep ache and throbbing pain of overdoing activity...for example working with trauma patients who have fractured hips, I have to lift and twist legs back into the hip socket.

Keep bags of veggies in the freezer for use as ice bags. Just buy a vegetable you don’t normally eat. Okra comes to mind, but peas mold easily to the shape needed. Put one or two Ziplock bags over the veg bags as they can leak.