Hello, and welcome.
I'm so sorry that Zeke is having a problem with his left eye. The swelling and discharge may be symptoms of an eye infection or the result of an injury, like a scratched cornea. The third eyelid showing is not unusual when there is a problem with the eye, itself and/or there may be illness in the body, in general.
If Zeke is currently being treated for his allergies with steroids, his swollen eye may be the result of his allergies or it might also be an indication of the feline herpes virus (FHV). The herpes virus in cats is not communicable to humans and typically occurs with upper respiratory symptoms, and frequently affects the eyes. To ease a 'flare-up', if he DOES have FHV, L-lysine is very helpful. They make special formulations for cats that you can find in your local pet supply stores, in natural food stores, like Whole Foods, or order online:
There's no doubt that he should be seen by a vet, as soon as possible, to get a diagnosis and appropriate treatment, but for the moment, gently clean away the discharge with a slightly dampened cotton ball.
If the situation seems to worsen tonight, bring him to the nearest ER vet center so he can be evaluated and treated, in person.
I hope all will be well with Zeke and he's a lucky boy that you choose to rescue him a few years ago!
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