To have an alternative address you need to open a new mailbox, this would be your account name with "_1" after it. If you log on using that address, you can send e-mails totally separated from your primary e-mail account. You can use an alternative name (Alias.), but must log on using the account name and password.
I use this arrangement to provide my daughter with a mailbox as her ISP does not provide one, the only drawback is that she has to go to BY's e-mail site to send anything as she is not on BY.
The problem with selfcare may well have been cleared up by the time you read this, if not, contact BY and get them to fix it. I have found them to be very helpful when I've had any problems.