OK, in order to change the DNS address in the S3, my guess is that you had to set it to not use DHCP, which almost certainly would have been the default setting. Risky, because you'd be forced to set up other things that don't need changing.
If you didn't know, all DHCP does, in a nutshell, is to set up devices on the LAN with a bunch of IP stuff that lets the devices talk amongst each other, and to communicate on the internet. On a home LAN, all these details live in a single, central "DHCP server" that serves the IP gubbins to each "DHCP client. At home, this DHCP server runs in your router box. In turn, your router connects to a different network that is part of your ISPs network, and it gets its own IP details for using the ISP's network, in a similar fashion from server on the ISPs network (I'm simplifying). Part of what your router gets from the ISP is thing called a DNS server address. All the DNS is about, from your point of view, is a means to translate a human-rememberable name, such as google.com, into an IP address, by looking it up in a big database.
All clear so far?
Your mission, should you choose to accept, is to point a browser from a phone or PC on your LAN to your router and find the page on its internal web server that deals with internet networking. That's where DNS and more will be found - normally set to "automatic". This is the place where you override that with the 1.1.1.1 number - as a test. Nothing destructive will happen. You can set it back to automatic later if it's not helping.