I want to offer some additional "opinion" to your situation.
Coughing and blood: this may not necessarily mean infection. And the source of bleeding can be anywhere in the airway-lung. A "mild" bleeding is merely caused by irritation and dryness and a broken vessel in the trachea or upper bronchi. Not to say that it's NOT an infection, but rather to give an alternate view.
And yes, for some CFers, Pulmozyme causes bleeding.
Appetite: inflammation of lung tissue CAUSES decreased appetite. Get the inflammation reduced, and you will likely see an increase in appetite.
Pancreas: there are two functions: endocrine and exocrine. Don't forget about blood glucose levels. Your daughter may have sufficient ability to produce enzymes for digestion, but may not have adequate insulin production. Insulin and bg also have an effect on appetite.
Not to offer insult to Americans who have posted, but the reality of healthcare, whether public, private, or insured, is that CF Clinics and doctors are in BUSINESS. The most basic economic model that all will follow in order to maximize profit is to keep you alive, but not well. A relative amount of "sickness", to insure repeat business, is the only trusted model. I think that the only way to find true altruism in medicine or health care is that you will never find it.
Therefore, with relatively few CF patients in Japan, you will likely do better at finding healthcare professionals who are genuinely interested in treating your daughter, rather than maximising profit.
I am Canadian and have lived in Ontario, Saskatchewan, and Alberta. Don't be fooled by the myth of "universal healthcare". This public insurance system only insures access to a hospital ER, and access to a physician, without expectation of payment. EVERYTHING beyond that requires payment, co-payment, or insurance. In my experience, the public insurance is woefully inadequate, unless you plan on being on welfare/social services for you, your family, and for your entire life.