I am getting the same thing, I literally just started the account, I have everything I need a single folder to upload to the website but I cannot for the life of me get it to actually upload anything, I can use the uploader via cPanel but it is clunky, I just want to use Filezilla but I get the error of 552 Disk full each and every time no matter the file size.
The 552 (or error 28 from MySQL) means that the shared disk space on your server is nearly full. It's not (or at least not necessarily) related to your account in particular. cPanel operations and all disk writes from user accounts are disabled while that situation exists in order to prevent file corruption. An admin will have to free up some space (or, in some conditions, provision more disk space for the server).