By default Windows stores user profile data within the c:\Users<username> folder. Because this default location is on C: which is often the system drive, the drive can easily run out of space. Moving them to a different drive using a junction addresses this problem.
To do this, a user's files have to be moved to a different location and then delected from c:\Users so a junction to the new location can be created. But a user can't delete their own files because they are being... used.
If its possible to boot to safe mode then this is an option but on a live server this may not be an option. In such a case, another administrator can do it for you but can it be done without requiring a different admin? Yes but the account being used does need to be a member of the Administrators group.
First change the registry entry for your user so it points to a nonexistent location. The registry key for all user profiles is:
HKLM\SOFTWARE\Microsoft\Windows NT\CurrentVersion\ProfileList\