Yes, JOT server will need to be installed on the new server; JOT has to be on the same server as your website. Are you sure the 15K visitors are not spammers that Cloudflare is blocking reaching your site? I doubt very much that your hosting company is blocking visitors to your site; and certainly not because you changed the name servers to Cloudflare. Your hosting company does not care what name server you use; it has nothing to do with it.