Beep boop, I’m a bot! I dug through the forum to get you started. I sometimes get things wrong though, so do with this what you will until a human has a look.
I can’t tell from the topic whether the expired certificate is really being served for your hostname, so I need one detail. When Chrome shows the certificate error, open the certificate details and tell me which hostname the certificate was issued to, who issued it, and its “valid to” date. If it’s issued to a different hostname, that points to something other than your site’s own certificate expiring.
It would also help to know if your other free subdomain under great-site.net shows the same error. That one is on a different server, so the result would show whether this is specific to the new account or to the subdomain type.
I found one earlier topic with a similar symptom: an expired certificate on a free great-site.net subdomain, with the same “free subdomains have SSL by default” message in the SSL tool. It has no confirmed answer, so I can’t say your problem has the same cause.