Tears spill from the eyes for two reasons: 1) increased tear production due to eye pain, whether from hair irritating the eye, a corneal ulcer, or some other problem; or 2) a blocked or malformed tear drainage system.
It sounds like Cosette’s veterinarian has ruled out increased tear production, so her tear staining probably results from tears spilling over her eyelids rather than draining internally.
Normally, tears leave the eyes through the nasolacrimal duct system, draining through tiny holes at the lower inner corner of each eye and exiting through the nostrils. A conformational abnormality, from a covering over the tiny holes to a blockage of the duct as it travels to the nostrils, may be responsible for Cosette’s tears spilling over her lower eyelids.
A veterinary ophthalmologist can advise you about whether flushing the nasolacrimal drainage system or corrective eye surgery will resolve the problem.
Or you can manage it by asking your groomer to keep Cosette’s hair very short beneath her eyes so the hair doesn’t trap her tears. Wash Cosette’s face daily with a warm, damp cloth. Consider applying a bit of petroleum jelly to the hair below her eyes so her tears slide off.
Probiotics sometimes help prevent tear staining. Try an oral veterinary probiotic such as FortiFlora, Prostora, or Proviable.
Don’t give Cosette tylosin, tetracycline, or any other antibiotic for her tear staining. Using antibiotics for cosmetic purposes may contribute to bacterial resistance and cause problems in the future.
An abscess, the most common feline bacterial skin infection, forms because cats have tough, elastic skin that quickly seals puncture wounds, trapping bacteria beneath the surface. As the bacteria proliferate and white blood cells flood the area to fight the invaders, the abscess swells. Eventually, it ruptures, releasing its thick, fetid, sometimes bloody, yellow-brown pus over the skin.
If you can catch your free-roaming tomcat, take him to your veterinarian, who will thoroughly clean his wound, insert a drain if it’s necessary, and administer an antibiotic. Your vet also can vaccinate your friend for rabies, test for the feline leukemia and feline immunodeficiency viruses that can be transmitted when cats fight, and neuter him so he’s less likely to fight and get bitten again.