I have a little to none experience in developing a plugin or widgets, but I believe this is certainly doable in a custom WordPress theme.
- Output an ajax multiple file upload form in the sidebar. Link
- Handle the file uploads and save them as attachment. Link
- After you get the attachment(s) ID, save them as an array in the user’s meta e.g ‘sidebar_image’. Codex
- Back to the sidebar, check if current user already have the ‘sidebar_image’ meta.
- If she does have a value, then just create a attachment query, according to the meta value. Codex
If you want this method as a widget. The function on step 2 and 3 will be the same if you use a proper ajax method.
Hope this help.