Try teamviewer to a computer in your network..
You cannot access the NAS directly but via remote desktop to the computer it is sometimes possible to do it.
The statement that you had a public IP was wrong..
I have a Public IP Address and my problem now is how to set it up.
You cannot access a system from outside in this kind of setup.. you do not have an internet routable address.
So one solution is to use a 3g or 4g modem/router with a public IP. Or a different ISP that does offer routable public addresses. Make very sure though before you buy it is truly public address.. many companies using 3G wireless for internet only give out private addresses. And charge a lot more for public IP.
But TeamViewer could still allow you to access your computer remotely.. and then access the NAS.. the speed might be horrendously slow because you are sharing the network with multiple users.. also the ports may already be allocated.
If there are files you need when you travel the best idea is to load them to cloud storage.. or carry files in a 2.5" USB drive.. which are cheap and light-weight plus self powered on any newer computer with a charge USB port.