When you say general library do you mean here in the Gallery? All images in the Gallery are public just like the forum posts, the only way to restrict the viewing would be to move them to a private album with restricted access or delete them.
If you want to move an image from the gallery into an album then follow these steps.
1. If you don't already have an album setup you can use this link to create one. Make sure to set the privacy to registered members only.
2. Then you need to select the Gallery images that you want to move, you can see your images under your main profile. Select the check box on the image itself (you can select multiple), doing this will bring up a bar at the bottom of the screen where you can select move, you then need to click 'go'.
3. You'll now see a screen where you can select Album and there's an option for existing albums.
Just remember that this will only move images in the gallery, if you have uploaded images in forum posts then there is no option to move these, you would need to delete them if you don't want them to be viewed by none registered members.
Also if you don't want images uploaded to the forums to be copied to the media gallery and also displayed in InstaView, then there's a checkbox under your account preferences to disable this. Just check the box: "If checked, images uploaded to the forums will not appear in the Media Gallery or InstaView".