The limitations that you described about 3G have always been that way. The 20MG download limit .... you could never download a movie over 3G since movies are way too big for that.
There is no way to work around it other than to find ways to connect to WiFi when you are out and about - or get internet service in your home and use WiFi there.
Here's what might be happening, and it may be simpler than you would imagine: the library has some type of login or splash page. Here's what you do. Go back to your wifi settings, tap on your library's network, and tap forget this network. Go back to your wifi settings and tap on the network. If nothing else happens, go to Safari, type in a website, and hopefully a splash page would come up asking you for your card number or just telling you their terms. Hopefully this helps!