Currently the BAA only allows members to upload images that are public to all. We don’t offer storage of private data, and I suspect it’s unlikely the BAA ever will.
The difference between public and private collections is simply whether the grouping of images is publicly visible or not. If you want to make a grouping “My favourite images of Jupiter”, for example, you can choose whether your member album page allows other people to see that grouping. In any case, the individual images will still appear in your album.
The “Add image” button at the top is used to upload images to your album, and not to add images to collections.
To add an image to a collection, you should navigate to the image in question, and scroll down to the top of the comments area, below the image. There you should find some controls to add (or remove) the image to/from your collection(s).
Hope that helps,