I would wipe it with some Boric Acid solution, (mix Boric Acid with water, a weak solution) or even Saline solution like what you would use for contact lenses, then apply an antibiotic ointment to the eye.
I'm not sure what you would have available. In any event, try to gently wash out the eye in case there is something in it.
Can't see what is going on in the eye itself, but I would first look for any foreign objects in there, such as a sticker or something else, check the 3rd eyelid as well.
If the color part(center) is white or ulcerated, it is most likely pinkeye.
And must be treated right away with LA200 drops in the eye.
If you see white(cloudiness) anywhere else or ulcerating, it may be a scratch or something in the eye.
Check around that area, what ever it is must come out.
If you do find something in there and get it out, then put a few drops of penG or LA200 in the eye for a few days.
If it is a scratch or something really in there and you can't get out, depending on severity, a vet should see the goat.
They can put drops in the eye to see what is going on on there.