Each time any of mine have had hay pokes its always been out of hrs

If the hay looks like its still there I would try the tweezers or tissue methods as above. As long as it looks like it will come away cleanly (cause no more damage than already done)
...if its actually stuck in the eyeball ring the vets now as a matter of urgency!
If not actually in the eye, but on the surface I usually have an egg cup of boiled water with a pinch of salt added, then cool down the water. If u have a clean syringe just gently dribble the solution into the eye to help sooth &clean it out.
If no syringe available I usually have a strip off of a clean paper kitchen towel, dip in the solution &gently squeeze the wet kitchen towel making the solution drip into the eye from above.
An extra pair of hands usually easier than trying to do alone!
This should suffice until morning but a vet visit will be needed tomorrow to check for ulceration&damage &any possible foreign body still remaining under the eyelid.
If u can't get an appointment until tomorrow pm u can give another eyewash with fresh solution.
The quicker eyes are treated, the less damage &complications occur leaving a much greater chance of a full recovery (within a week in most cases.)
Speedy recovery. Xx