GoDaddy does not support installing self-signed SSL certificates in shared web hosting accounts, as can be confirmed from this thread: Does shared hosting support installing self-signed certificates?.
GoDaddy's shared web hosting accounts use a custom control panel (not cPanel, Plesk, etc...) that doesn't provide the option to install SSL certificates. They need to be provisioned by their SSL department and installed on a shared web hosting account with a dedicated IP address. When you order an SSL with them, they'll convert your shared web hosting account from using a shared IP address to using a dedicated IP address.
If you upgrade your shared hosting account to a VPS or dedicated server, you will be able to use a self-signed SSL certificate (either with cPanel or Plesk as the control panel, or manually since you'll have root access).
It is possible to add a self-signed SSL to a shared web hosting account with a dedicated IP address, but unfortunately not at most web hosting companies that use custom control panels (as many larger ones do to save license fees, streamline options for users, etc...).