"It's basically impossible to make a reasonable guess at what's going on" is what I have to tell my poultry owners far too often. Unfortunately, the symptoms you've mentioned can indicate any number of illnesses or health issues. In avian medicine, there's rarely one cause of a condition, so we usually begin with a list of differential diagnoses and use lab tests, X-rays, and physical exams to differentiate one from another. With this in mind, your best course of action is to reach out to your county-extension poultry personnel or avian-oriented veterinarian (please see here: www.aav.org) for help in differentiating the various causes of what you're seeing. Veterinarians can perform a physical exam and run diagnostic tests, including X-rays, to distinguish between the various etiologies.
It's best to approach the diagnostic process with a clear sense of your hen's financial value to your operation. Although some services such as your county animal disease diagnostic laboratory might be available free of charge through a county agency or land-grant extension office, the expense of some diagnostic tests and treatments can add up quickly. While it’s always worth your time and money to identify a bacterial or viral infection that could potentially impact more than one member of the flock, this might not be the case with a condition that only affects one hen.
The best clue is her "constant, rapid breathing" which suggests lower respiratory compromise - pneumonia, e.g. If I were to presumptively treat her, I would dose her with injectable Tylan-50 given orally at 0.5 ml once daily for 5 days and see if she responded favorably. If so, I would continue the Tylan for an additional 5 days. She should be brought inside and kept in an 85F environment and force fed a "recovery food" such as you might feed a baby bird: http://www.kaytee.com/products/exact-hand-feeding-baby-bird.php/
Please respond with further questions or concerns if you wish.
Remember, when you lose a bird it's best to have it necropsied in an attempt to determine the cause of death and then be able to treat the rest of your flock if possible.