Hi Janek Holmik your connection is probably behind a firewall. You will need to fiddle with your router settings to allow the Nintendo Switch free access to the internet and/or bypass your security. You can set it at port level or your security level. The settings differ from models of routers to different versions as well. Also it is a little bit difficult to explain if you aren't sure how to access the router either. Try checking with someone who knows how to configure your wireless.
Alternatively you could borrow a USB to Ethernet adapter for the Switch and try a direct connection.