FIrstly, a strain and a "pull" are the same thing. And technically, a muscle strain is tearing of the muscle fibers - to what degree of tearing will determine the significance.
In terms of you calf, I would work on active pain free range of motion of your ankle and try to get back to a normal, full weight bearing gait. Once that is achieved, you can progress your exercises involving the calf. Ice and elevation are find to perform at this moment. Icy hot is not going to do much more than maybe decrease the pain due to the analgesic. Advil will help with controlling inflammation.