Greetings,
Thank you for asking.
Before moving to Cloudflare, were your sub-domains working over HTTPS connection? 
May I ask if they are like example sub.domain.com or www.sub.domain.com?
May I ask what SSL option have you got selected under the SSL/TLS tab at Cloudflare dashboard for your domain ( Flexible, Full, Full Strict … )?
Not sure if it’s HTTP(S) issue, if so:
May I ask have you tried using a different Web browser, or tried clearing your Web browser cache?
How about using a Private window (Incognito mode) or a VPN connection if possible?
Is it the same behaviour on your mobile phone (4G LTE, mobile data, cellular)?
And it’s pointed to the correct IP address, therefore status is proxied 
?