Often cats that are ill will have their third eyelids elevated. This may be the reason your vet suspected worms (although I would assume there were other circumstances that would indicate a presence of parasites). When cats have injuries to their eyes, the membranes will elevate.
I've seen this time and time again with cats that have foreign bodies in the eye (foxtails or other plant awns) or injuries to the cornea (scratched by another cat, for example). If you are not satisfied with any answer or treatment you and your cat receive from your vet, I would get a second opinion and have the eye stained and thoroughly examined. I hope your cat is better by now!
My first thought is that your cat has an infection in its eyes. Possibly they are irritated by something environmental in your home, or she has scratched her eye. If it is both of her eyes that are affected, I would would go more of the "infection" route.
Your vet should prescribe some antibiotic drops for your cat's eyes. The worming idea is interesting. Never heard that one.
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