If your server IP address is the primary DNS server IP address in your network settings, your machine is using that server for DNS.
One way to check is to create a DNS entry on your server for something like testdns. Set the IP address to your machine or an internal webserver. If it is for an internal webserver, you can navigate to it by typing http://testdns in a browser. If it is your machine, ping to testdns. That will verify that your machine is using your internal DNS server.