Thinking about it from a survival stand point, a rabbit wouldn’t close its eye unless it was to relieve some pain/discomfort. Vision is really important, so if your rabbit is insisting on it being closed, I think this does require a vet visit. Something that causes your rabbit to keep an eye shut, whether it’s a nail scratch or hay in the eye, is best assessed by a rabbit vet to see if the damage needs treatment. I can imagine even “minor” causes of eye discomfort (hay piece) can cause damage that requires veterinary treatment.
Rabbits can have stray pieces of hay irritate an eye, be in an eye, and there are also eye conditions that come from the inside (not necessarily caused by outside stimulation) and those may not be apparent from the outside, but inside, your rabbit may be feeling inner pressure or pain.
Best wishes to you and your bun that it’s nothing serious.
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.