My left ribcage is bigger than my right. Is it normal?

Possible scoliosis. It is not terribly common for one rib cage to be noticeably larger that the other, but what is fairly common is to have some degree of what is known as an asymmetric trunk rotation. The trunk is rotated making one side appear larger that the other. It is often associated with scoliosis of the spine so you may want to be seen and checked for that.