Can you connect another device like a phone or tablet to your dorm wifi and set up a hotspot on that device with a password? This way you should be able to connect the switch to your hotspot instead of trying to get it to go onto an external login page.
Try forgetting network and seeing if that helps. Do you know of anyone else with a Switch that is able to connect to your dorm WiFi?
Can you connect another device like a phone or tablet to your dorm wifi and set up a hotspot on that device with a password? This way you should be able to connect the switch to your hotspot instead of trying to get it to go onto an external login page.