Your requirement can be achieved by Smart Members Pro and Channel Images plugin. I am assuming that your website have
User section from front-side and
Admin section from beck-end to manage that
Using Smart Members Pro :-
You should create
Member's Registration, Login, Update profile, Change password, Forgot password and reset password by using this plugin. For member area in EE this plugin is supreme. So, that you can create separate member area for every registered User.
Using Channel Images :-
After making any Channel (having Channel Images field) to store images, You should make front-end form to upload the images by
logged_in User by using
Channel form. So, that user can upload the Images from front-end.
By this way Member section can be handled by
Smart Members Pro and Upload images section can be handled by
Channel Images. And to assign Images to any member you can create
Simple Text-box and store respective member-id into it. Combination of these two plugin can achieve your requirement for sure.