I'm going to try and give her a warm bath.
Does anyone know what causes this and what I can do to help her? Any help would be very much appreciated.
It sounds a bit like coryza with both eyes being affected, and the bad odor. This is a chronic contagious respiratory disease, and any chicken in the flock will be a carrier. Sulfadimethoxine and Sulmet can be used to treat symptoms, but cannot cure the disease. IOt can recur with any stress in the flock, such as cold weather, moving, or molting. Any pus in the eyes must be removed and eyes flushed with saline. Any sick chickens should be separated from the flock. Culling sick chickens may limit the disease. A state vet can confirm the disease with a necropsy. Here is some info to read: