When the member logs in to their "area" you would assign a session variable which would be their unique ID in the "members" database table.
When you save the record of the file you upload you can store this session variable in the table, so the database knows that it was uploaded by this member.
Then when you pull the records back you filter the recordset only to show records that have a memberid of the session variable set at login.
If you want you can also create a directory on the web server named as the unique ID so that all member uploads are stored under their own directory.