Hi and welcome to PCHF!
I would recommend you use this:
No-IP - Dynamic DNS, Static DNS for Your Dynamic IP
You can install it, and since you don't have a static IP, all you have to do is go to YOURCHOICE.no-ip.info as the IP and it will always be updated.
The reason that you cannot access it, is because you probably don't have the ports forwarded in your router. You will need to give the server a static IP internally. I'm not really sure how to explain this because I don't really mess around with Linux too much anymore.
I hope this helps.
Regards,
Adam