We can't really help with the cPanel configuration. That's a bit out of our wheelhouse and every hosting company is different. I'm sure GoDaddy has a lot of documentation on how to install your own SSL certificate, but it would depend on your plan and a lot of other factors.
Beyond installing your own though, you may want to consider something like Cloudflare. It's free (though they have paid upgrades) and comes SSL by default. It's not another hosting company, it's basically just an in-between between the user and your website. It's also good at speeding things up.
I hope that helps, but if you need anything else, just let us know.
Thanks,
Alex