There could be something added to your page only when logged in. That something could be coming from a third-party plugin.
You could try testing for a plugin conflict. You can do this by deactivating all third party plugins, and seeing if the problem remains. If it's fixed, you'll know a plugin caused the problem, and you can narrow down which one by reactivating them one at a time.
If that doesn't help, please give us WordPress Admin access in a Secure Note so we could check what's happening when you're logged in.