If you have to shoot with one eye closed, you may be cross-eye dominant. If you're shooting right handed, but have to close your left eye, you may want to consider shooting left handed. Then you can keep both eyes open. It's not as crazy as it sounds. I've shot shotgun right-handed all my life, but switched over with the bow and inside a couple of weeks it was feeling as natural as shooting right handed.
It's definitely worth checking to see which is your dominant eye.