Yes, of course you can. In my opinion, it is a good way to have some ice on your injury eyes. Anyway, I think I can give you some advices which can help you know how to heal your eyes and make your eyes recover faster. The ice is to assist the blood to flow easier in the area that has been injured. Ice or cold compresses can help to reduce the swelling or inflammation in the area. Thus, the blood will flow and the vessels that were damaged will begin to heal. While when the injury eyes won't heal, it could mean that the damage is extensive beneath the skin. And another reason for slow-healing injury can be an iron deficiency (such as anemia).so you should make sure that your injury eyes would not be infected.