Hi there, welcome
It sounds like he might have cherry eye, or possibly something going on with his tear duct. Can you post a photo? Cherry eye is when part of the tear duct prolapses, and can be fixed surgically (it’s not too terrifying though).
My bun had cherry eye surgery before, and occasionally we see part of the tear duct. It looks worse some times than others. So, it might not need to be treated right now, but you should still get your vet’s opinion on what should be done (and confirm what the issue is).
If it is a clogged tear duct, the vet can flush it out. An infection would likely be treated by some eye drops.
His eye also could have been irritated a bit by the clog, making the duct more obvious.
My other bun’s third eye lid has also gotten a bit red and irritated from dusty hay, so that’s a possibility as well.
Let me know if you need help posting a photo so we can advise a bit better.
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The answers provided in this discussion are for general guideline purposes only. The information is not intended to diagnose or treat your pet. Seek the advice of your veterinarian or a qualified behaviorist.