Running your own named is overkill and not needed. Here's what a valid setup looks like:
- Your web server hosting provider (where your website lives) gave you some DNS resolvers. These are intended to provide DNS resolution to your web server, so it can find OTHER hosts on the Internet. These resolvers have nothing to do with hosting YOUR domain, and you cannot make changes to their domain definitions.
- Your DNS Hosting Provider has their own DNS servers, which are used by default to host your DNS "A" record. If you truly reconfigured your DNS hosting account to use the web provider's DNS servers, this is an error. You cannot add your DNS record to those servers.
- On your DNS Hosting Provider's control panel, first set it back to using their DNS servers; then create an "A" record for your domain, pointing to the IP of your web server host.
In summary:
DNS Hosting Provider
DNS Server(s) contain:
www.yourserver.com A 1.2.3.4
alias.yourserver.com CNAME www.yourserver.com (maybe)
yourserver.com MX where.you.receive.mail (maybe)
Web Hosting Provider
Your web server at 1.2.3.4
/etc/resolv.conf
nameserver 1.1.1.1
nameserver 1.1.1.2
nameserver 1.1.1.3
That's all you need to do for other people to be able to find your server.
The only reason to run your own DNS would be to host an entire network consisting of multiple machines, behind a firewall, or hosting an entire Class C or greater set of IP addresses. To do this you'd need peering and routing agreements with other providers, which I don't think you have.
EDIT
$ dig duckfusion.com
; <<>> DiG 9.8.2rc1-RedHat-9.8.2-0.17.rc1.el6_4.4 <<>> duckfusion.com
;; global options: +cmd
;; Got answer:
;; ->>HEADER<<- opcode: QUERY, status: NOERROR, id: 32080
;; flags: qr rd ra; QUERY: 1, ANSWER: 2, AUTHORITY: 5, ADDITIONAL: 17
;; QUESTION SECTION:
;duckfusion.com. IN A
;; ANSWER SECTION:
duckfusion.com. 1800 IN A 87.117.219.53
duckfusion.com. 1800 IN A 192.31.186.140
;; AUTHORITY SECTION:
duckfusion.com. 172800 IN NS dns4.registrar-servers.com.
duckfusion.com. 172800 IN NS dns5.registrar-servers.com.
duckfusion.com. 172800 IN NS dns3.registrar-servers.com.
duckfusion.com. 172800 IN NS dns1.registrar-servers.com.
duckfusion.com. 172800 IN NS dns2.registrar-servers.com.