How do I cover a sore on my dog? Written by Russel in A How do I cover a sore on my dog? You need to cover the wound lightly. First, place a sterile dressing over the wound then gently place a dog sleeve over it. The covering should not be too tight as it prevents the skin from breathing. Russel A pet owner who loves to share useful facts and information about animals. For now, I write mostly about dogs and cats.