I do not think you need to delete and start over but I also cannot see the configuration to see what the issue is.
Here is an example of an apex and www subdomain configured correctly:
Both apex and www are configured to proxy to site-name.netlify.app via CNAME records. That is a working proxy configuration above.
Have you tried doing something similar with your domain at Cloudflare? If so, would you be willing to please share a screenshot of the settings here?