First, I would recommend not icing.
Gary Reinl’s book ICED is a great resource on it.
People, We’ve Got to Stop Icing Injuries. We Were Wrong, Sooo Wrong | Community Video
(A year later) Peoples, We’ve Got to Stop Icing. A Year Later…. | Community Video
Original MD that coined RICE reversed his position
Have you looked up stream at the elbow?
The cause may originate there.