Applications read `/etc/resolv.conf` when they start. If you've changed that file, you may need to restart applications that access the network. Restart Firefox.
To avoid this inconvenience, you can run a local DNS caching proxy, put `nameserver 127.0.0.1` in your `/etc/resolv.conf` to point applications at your proxy, and configure your proxy however you like. This has the added benefit of making DNS requests faster. Dnsmasq is a popular choice. See No DNS on Debian wifi after unplugging the DNS cable and Process calling getaddrinfo() at boot gets permanently stuck with bad /etc/resolv.conf? for examples.