domain name system – DNS entry for the intranet site through godaddy?

I have what I think is a fairly new question. Wrote a simple site on asp.net. Published locally and I have to work with IIS 7, I think. We decided to launch it on an IIS server that we have and it works through something like:

http: //servername/default.aspx

However, I wanted to change the "Edit Links" to be assigned a name of dns or alias like mysite or mysite.mycompany.com. However, I believe that our DNS is managed by Godaddy, I do not know if we have a real internal Windows dns server. So I think I could not just create an "A" record in GoDaddy and correctly point out some internal IP address of my server?

I tried it and for me it just does not make sense, does it not work because I think Godaddy can simply be used for external sites? Maybe I just need to install a server or a DNS function on the server to allow me to create a DNS entry for this application?

Any suggestions will be appreciated.