What do you get when you do a "nslookup <yourdomain.com>"?
If you get an address back, then someone already has your DNS taken care of. If you don't get an address back, then either your domain record is not hosted on anyones DNS or your domain is invalid.
You can check your own domain record information by visiting the following link (if it is a .com, .net, or .edu) and searching for it;
When you do a "domain" search for your domain, it will tell you the responsible DNS servers for this domain. If those DNS servers are your static IP's then your need to host your own DNS server.
You don't need permission to set up your own DNS server, unless you are part of an organization that regulates your network (corporation, ISP, etc...). There are many considerations to take into effect if you need to put up a DNS server, you may want RTFH (Read The Friendly How-to's) for help on this.