Hi D,
I've heard of this constellation of symptoms once before, but for the life of me, I can't remember the exact case or ultimate diagnosis. I do recall that the person was dealing with an extremely rare auto-immune disorder. Another possibility that comes to mind is an in-born error of metabolism, where your daughter could be lacking a crucial enzyme to convert a specific amino acid or set of amino acids. This could cause accumulation in organ tissue, resulting in functional impairment, which could account for the bleeding you're seeing (chronic nephritis of some kind?). Build up of certain amino acids can also result in a nutritional deficiency or collagen synthesis disorder that could account for the itchy, blood skin, swelling lips, etc. (This is all conjecture, however). If the case and disorder come to mind, I'll write again.
I agree that you need to see another doctor, though. In fact, you may need to see a LOT of doctors before you find the one specialist who has seen a similar case and can diagnose your daughter.
I suggest starting with a medical teaching hospital, such as David Geffen at UCLA or USC. The medical professors at one of these places are far more likely to be in tune with rare diseases and are more likely to have seen a number of mystery cases. I suspect it will take a team to figure this one out.
Another suggestion I have is to contact the NIH. Contact the Office of Rare Diseases and request access to their Undiagnosed Diseases Program: http://rarediseases.info.nih.gov/Resources.aspx?PageID=31. You might also contact NIAMS (National Institute of Arthritis and Musculoskeletal and Skin Diseases: http://www.niams.nih.gov/) and NIDDKD (National Institute of Diabetes and Digestive and Kidney Diseases: http://www2.niddk.nih.gov/), and possibly the NIH Clinical Center: http://clinicalcenter.nih.gov/. Someone at one of these centers should be able to get you to the right place.
Good luck. It will take quite a bit of perserverance and advocacy on your part to find the right doctor(s) who can help you figure this out. My daughter had pain and numbness in her leg and hip for over 7 years. In that time, in addition to her pediatricion, I took her to see at least 4 or 5 orthopedists, 3 different chiropractors, and several physical therapists. I finally found an orthopedist at Cedars-Sinai who was able to diagnose the problem, followed by referals to 2 leading neurologists who were able to confirm the diagnosis (pyriformis syndrome) and propose the appropriate treatment (temporary paralysis of the affected muscle with Botox followed by physical therapy, then expert chiropractic care). Fortunately, no permanent damage ensued during that time, and my daughter has normal movement and feeling in the leg -- no more pain! You just have to stick with it, and don't take "it's probably something genetic" as a final answer. It probably IS, but you need specifics, not generalities. Docs often will not admit to not knowing the source of the problem, and will tack on the closest label that fits out of convenience.