You can issue and renew your certificate using DNS validation instead. This is the only workaround available if your ISP doesn't allow usage of ports 80 and 443.
But your current DNS provider (noip.com) doesn't make this easy. Their free service does not allow creation of TXT records, and on the paid plans I don't think they provide an API to modify TXT records, to facilitate automatic renewal.
There are other DNS hosts that make this easier. For example, Dynu is dynamic DNS provider that is supported by a number of Let's Encrypt clients, such as acme.sh.