I have a Windows 7 computer connected to a Verizon T1114 router. This router allows me to get a new IP address at will simply by logging into the router and rebooting it, since this router is connected with a SIM card and has a data plan. The issue I'm trying to solve is being able to use this computer as a Proxy server for other computers. I tried setting up NO-IP.com dynamic DNS on the machine, but the problem I'm facing is that because I'm not using a static IP, I cannot access the computer from the outside internet(according to Verizon). I tried putting the computer's IP address in the router's DMZ, and tried to forward ports as well, but when I try to ping the public IP address, I get request timed out.
The goal is to be able to have 1 computer able to get a fresh IP address at will, and have many other computers able to use that machine's IP as a proxy.