Just for terminology, the network name of a wireless access point is called the SSID. In your case, the SSID of each access point has been assigned the same value (i.e. the same name)
As you noted, the MAC address of each access point is unique. fyi... The different access points
may also possibly broadcast on different channels. An easy way to find all this out is download and run
NetStumbler to find out about all the wireless networks around you.
I'm going to guess you're running XP and using XP's wireless configuration tool (called Wireless Zero Configuration service). The bad news is the Wireless Zero Configuration tool only allows you indicate your preferred SSID (not MAC address or preferred channel). And i believe it just connects to whichever one has the strongest signall. HOWEVER, your wireless adapter's vendor
probably offers their own configuration tool which often provides the functionality you want (at least allowing you to distinguish between multiple access points/same SSID. Not certain about automatically connect to whichever has the Internet connection.
But at least can check on your options via vendor configuration tool as well as your adapter settings. If you'd tell us your Operating System along with make/model of your wireless adapter can see what options you have. Tho, you may also want to check with your school as many students must deal with the same situation and i would think the school offer some guidance/solution.