It is really painful for you to get wood in the eyes. You should better use the finger to make the wood out of the eyes. Then you should use the clean water to wash the bit of wood out of the eyes and then dry the eyes with clean cloth. You should not get the bit of wood in your eyes by accident. It is very dangerous which may cause the damage of the cornea.
Yeah, it really hurts when wood gets into the eye. Under such circumstances, don't rub your eyes, otherwise, your eyes may get hurt, making the situation worse. You can turn over your eyelid gently to find out the wood and remove it with the medical cotton bud. Then drip some eye drops in case of inflammation.
The best and natural way is let the tears flush the wood chip out of your eye. If it doesn't work, then flush the eye with eyewash solution or water. If you can't do it by self, you should seek help from others. If the wood chips still in the eye, you need go seek help from you doctor. There are something you need to pay attention. First of all, don't rub your eye. You may feel uncomfortable, but rubbing your eye may cause more injuries in your eye. Second, if the wood chip is a big one, don't hesitate to seek medical treatment immediately. Your eye may get infected by the wood chip, so get some anti-infection drops.