Is Mortin And Pressure Bandage Right Solution After Injury By Chain Saw?

Chain broke on our chain saw and made a small, deep cut on my son's wrist. He got a couple of stitches, and said to keep pressure on it because it may have got a small vein. He had to go back to the ER tonight because of golf ball size blood under the skin from bleeding more. They left it alone and put on a pressure bandage and sent him back home. He is going to take motrin for pain in his arm and go to bed. Is all of that ok? No clot will travel or anything, will it?