You are correct. Poultry eyeworm is a roundworm.You can also get roundworms in the eye, I’ve seen it in mammals (blech!!!) and I didn’t know what I was seeing....various google sources say it’s possible in horses, cattle, dogs but very uncommon. A fecal float is a first step for sure.
It is of course possible to get junk in the eye, a feather fragment, thread or hair....I pulled a 4” white pine needle out of my dog’s eye once, it was all the way in and only a small piece was poking out of the corner, she showed no distress before or after