DUMP that water!
Acetaminophen (tylenol) is a BAD choice for pain relief in a bird, dog and especially cat. Dump the water, do not use this. You may have harmed your bird, depending on how much you used. Pain relievers are not interchangeable especially, when you use them in different species. The previous BYC folk recommended aspirin- NOT tylenol or advil. It would be great if you could take your bird ASAP to a vet for an x-ray to see if the wing has any hope of healing, get appropriate avian safe pain meds, competent wing wrap if fracture is amenable to this, appropriate antibiotics if dog mouth punctures are found, and be sure to tell them that you gave your bird acetaminophen so they can treat for that too.
If the bird was pulled under the fence by a dog, and mauled enough to break a wing, there are likely wounds you have not found- look under the wing, keel area, where the legs join the body. From your description, you have separated her, checked her poop and doctored her water- have you actually picked her up yet and inspected her all over?
DO it! She needs more help than watching and waiting.
Jess