K.T.
Its not unusual for babies to have a favorite side. So if you usually start on the right, try starting on the left when he is more willing to nurse since he is most hungry at the begining of the feeding.
Could he have an ear infection? Perhaps one ear is hurting if this is a recent development.
Not all babies turn away when they are "done" sometimes they like to suck for comfort long after they have emptied a breast.
One thing to keep in mind is that is not really necessary to nurse both sides during each feeding. The longer they nurse, the more fatty hind milk they get. Most women I know nurse new babies on one breast each feeding unless they are making a fuss about still being hungry.
Check out this site for fantastic resources on breastfeeding:
www.kellymom.com