Hahaha
Sorry I think it's funny :P Instead of banning your MAC they banned your library account? How do they know that it is really you?

They can't ban everyone from the network without knowing they are dealing with. How the mechanism works for logging in, what features do you get by logging in?

Maybe they stored the mac-address they found mitm-attacking their network. Then they looked up if one of their customer accounts signed in from the same network and banned that account. Or is that not possible? I have really no idea how the system work there...

In our library we don't have wireless network, only prepared computers which are locked to only be able to browse... No way to discover the underlying OS.

I really hope you learned your lesson now. Do it on personal devices only, some routers don't even recover very well without manually reset after arp poisoning.