My cat has green eye discharge and a swollen eye. Is it an infection?

Hi and thanks for using Petco Pet Education Center, formerly Petcoach! Sorry to hear about Trinidad. The most likely cause is an upper respiratory virus/organism infecting the inner part of the eyelids called the conjunctiva. There are a few viruses that cause this in addition to a few bacteria. Herpes virus, calicivirus, chlamydia, and mycoplasma are just a few of the organisms that can cause this in cats/kittens.
These organisms are NOT contagious to people but are contagious to other cats. Kittens get infected by their mom and many of them become chronic carriers of the viruses. Once the infection takes hold and damages the conjunctiva, a secondary bacterial infection can take hold which often is noticed by a green/yellow eye discharge. Other signs can include those similar to a common cold in people- sneezing, runny nose, coughing, fever, lethargy, decreased appetite, etc. The other possibilities for this include a tear duct problem, injury to the eye, etc. Your vet can take a detailed history, examine Trinidad and focus in on the eyes and look for other signs of an upper respiratory infection. They can stain the eye and measure the pressure inside the eye if needed. Staining the eye will tell if the cornea is damaged from either trauma or a viral infection. Your vet can then advise a treatment plan including eye drops/ointment, something for pain, possibly some antibiotics, anti-inflammatories, etc. Good Luck with Trinidad.