I have no idea what you mean by "internet stick", however if you mean internet dongles that transmit a 4G signal via a USB connection, they work yes, but your ping will be high (does anyone remember art aka godlike from aG/woop? he was using one and had around 120 ping from portugal to germany).
EDIT: art's adapter was 3G actually, maybe 4G offers better ping, not sure.

Since you speak about not being able to move your PC to the next room, is the internet connection you're getting to your router unstable or is it just the wifi? If it's just the wifi, you can use a powerline adapter that you can connect from your router to an electrical socket in your house. Simply plug the other end of the adapter (it's detachable into two parts) into the electrical socket in the room where your PC is, and connect the adapter to your computer via an ethernet cable. I'm doing it and I get totally stable internet speed (160mbps down/12 mbps up) although my ping isn't 100% stable, but it's always playable. If your connection is making it hard for you to play atm, I would suggest trying it.

If it's the internet connection that is unstable, I would suggest pinging your router via your computer's terminal to see if there's a problem in your local area network, or something external. If the results from pinging your router are more than 1ms, chances are you will need a new router (unless you're using the powerline adapter method I suggested above in which case it's normal). You could also try performing a traceroute to certain sauerbraten servers and see if you're travelling through an unnecessary amount of hops in order to reach the destination, or if one of the nodes you ping along the way is specifically very laggy, then that would seem to suggest it's an ISP routing issue, and aside from flushing your DNS cache or resetting your IP config, the only solution is to use a VPN while you play or change ISP.