When I asked my professor about which disorders cause red fingers, he listed so many of them -- arthritis, Crohn's disease, Raynaud's disease, fibromyalgia, multiple sclerosis, etc.
But apparently, the exact tone of the red is also important. For example, if the red is bluish, then it's a sign that there is a problem with the lungs. Oxygen causes the blood to be bright red. If blood doesn't have enough oxygen, it can turn a bluish red.