The greenish color is classic for Pseudomonas. The horizontal lines in the nails are called Beau's lines. Beau's lines may develop after any major metabolic condition. They may appear following chemotherapy or, as in this case, as a result of Graft vs. Host disease. A paronychia is an infection around the nail.
Many organisms can cause a paronychia.
This particular case is caused by the yeast-like organism Candida. Fungal infections of the nail are referred to as onychomycosis. Candida is a frequent cause of onychomycosis. Other fungi may be involved. This photograph demonstrates discoloration, friability, and crumbling of the nails.