Is it possible to create nameservers off of one domain and point them at different servers located in different places? Such as:

ns1.mydomain.com - Server 1 (Texas)
ns2.mydomain.com - Server 1 (Texas)
ns3.mydomain.com - Server 2 (Washington)
ns4.mydomain.com - Server 2 (Washington)
ns5.mydomain.com - Server 3 (New York)
ns6.mydomain.com - Server 3 (New York)

I am pretty new to the whole hosting/nameservers and want to know if this is possible. Thanks in advance for any help.

Yeah it is.
You have to log in to your registrar where you registered mydomain.com, and then find the menu where you create Nameservers.
You then put in the IP's for each server in each entry for ns1-6.
This will create glue records for those servers.
After that you should also add A-records for each ns1-6 entry to each IP, and you'll be good to go, just start delegating domains to them.