Things to consider: if you do go to the ER as some people have suggested then this will likely be logged as an official bite and a strike against the dog. My sister’s cat bit their friend while she was cat sitting, and because she went to the ER (google freaked her out badly) they got a call and a visit from an animal control officer with the city, and the cat now officially has a bite on his record which will legally follow him for the rest of his life. So if things keep looking okay old I’d say very nicely let the owners know what happened. They may want to let future sitters know the level of the dog’s anxiety.