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.
In most cases people apply cold pack because it can help reduce pain and swelling. And it is also apply to people with injured eyes. However, you shall not use the ice directly in case any localized frostbite. You shall use a a small wet towel to wrap the ice before to touch your skin. Nevertheless, ice pack can't cure your eye injury. So, you still need some medical way if you want to recovery your injured eyes as soon as possible.
Technically, cold applications to the structures around the eyes might reduce pain and swelling due to injuries or some disease processes. However, it is better to warp the ice in a small wet towel before utilizing the ice pack out of the freezer, to ensure a few layers of cloth are between the ice pack and the skin. Because applying the ice pack directly onto the closed eyes could cause localized frostbite.
If the eye surrounding parts get the embossing symptom, you can use the ice pack to release the swelling part. As we know, the ice pack will have the role of calming and stopping the pain. However too cold temperature may stimulate the skin which you should take care of.