Regarding nameserver change for a domain, if that was in between, usually it’s up to 24 hours due to DNS propagation.
I assume your “full” sub-domain is like sagarspeaks.yourdomain.com, is that correct?
Therefore, what kind of a DNS type record you added?
Is it an A or CNAME type?
Furthermore, is it being proxied via Cloudflare at your DNS tab - or cloud next to that hostname (subdomain DNS record)?
Does anything change if you switch from to , or vice-versa?
404 error
What kind of an error do you get?
Have you tried flushing your router DNS or restarting your router?
How about clearing Web browser cache?
404 error usually comes from your web origin host/server.
Nevertheless, it could also be related in someway with an SSL setup and settings.
May I ask what kind of SSL option have you got selected under SSL/TLS tab at Cloudflare dashboard for your domain? (Flexible, Full …)
or 
cloud next to that hostname (subdomain DNS record)?