What I should have done was just let go of the leash because I still had the handle looped around my wrist. I still could have controlled him and prevented him from running after the dog. I would have been able to prevent my rope burn also. Oh well, chalk it up to experience, but because of this incident I had to cut our walk short to nurse the rope burn. I was lucky that the leash did not break any skin but I immediately got blisters on four of my fingers. The blisters felt like they were burning so I could not handle the leash in my hands anymore.
In case this ever happens to you just dip your hand in cool water for a few hours. I had to keep changing my water and once in a while add a cube of ice but the burning sensation disappeared after 3 hours of this therapy.