My website does not work with www. Please help! This only started after migrating to Cloudflare
May I ask what’s the error code you’re seeing?
May I ask you to post and share the URL example to the particular resource in a bracketed dot [.] notation with us so we could double-check, troubleshoot and provide some feedback information? 
Was there some kind of an redirection from non-www to www or vice-versa?
It could be you might be missing the A www DNS record under the DNS tab of Cloudflare dashboard for your domain name
If that’s the case, then below article could help you to double-check this and re-add it if it’s missing: