Congrats on your new dog! And I second BenMaxs comment - good for you for adopting an older dog. It sounds like she led a rough life previously to finding you, poor thing.
If the vet has ruled out medical issues, chances are she's just never really been worked with properly to learn how/where to house-train. She may also have been kept in a crate for long periods of time and has learned that it's "ok" to pee there, and on herself. :sad:
As BM suggested, keep her on leash with you when you are going to be distracted. You may have to resort to training her as you would a puppy - which means she goes out after eating, after playing, and when she wakes up - constantly, through the day.
I rarely advise against crate-training, but in her case - it may be neccessary to avoid having her pee; and the whole success to house-training is to keep from giving them the opportunity. If she HAS been kept in a kennel and has learned to pee in it (and on herself) - simply because of her age, it may be more productive to do away with the kennel and find a different area to keep her in.
"If you are a dog and your owner suggests that you wear a sweater. . . suggest that he wear a tail."
Vali (American Bulldog)
Artiro (Cane Corso)