What kind of eye drops have you been given? With our prompt treatment eye removal is thankfully not a real risk - let me assure you!
This is how Begw's eye currently looks. I have already been able to get rid of most of the surface ulceration on top of the eye, apart from the small area where the hay stalk has penetrated but there is still quite an amount of infection in the chamber below the surface. Thankfully neither the stalk nor the infection has penetrated deeper into the eye.
So while this is looking rather alarmingly right now, it should actually all heal up again perfectly again!
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Begw is on chloramphenicol antibiotic eye gel (which is the stronger of the available antibiotic drops/gel), metacam for painkillers/inflammation and on plain artificial tear gel for lubrication, comfort and healing support.
A smaller hay poke doesn't necessarily show up to the naked eye (unless there is a lot of eye blinking and watering, which is always a warning to have the eye checked) until it starts to ulcerate by creating first bluish dot over the penetration spot (or scratch if something has got stuck under a lid) and then a film of infection gunk on the surface of the eye. Ulceration can happen in a matter of just hours and get much worse very quickly. The deeper the infection can spread into the eye, the harder it is to get on top of it. The last resort is enucleation (eye removal).
That is the reason why you should never underestimate a potential eye injury and see a vet promptly as soon as you can within 24 hours with a minor injury, as an emergency as quickly as possible if there is blood.
After I had eight hay pokes in 2018 (some of them even nastier looking ones), I have always plain tear gel from a pharmacy at home. It can only be applied at least half to an hour after any antibiotic drops to allow them to be fully absorbed and not be washed away, but the tear gel can be applied up to 6 times a day.