Have I broken my pledge?

Chicken broth is made from chicken, and is not considered vegetarian. It has a very distinct flavor, and I find it surprising that you didn't know what it was the moment you ate it. That being said, chicken broth has been PROVEN to contain many nutrients that your body needs when sick (and it helps replace any of the nutrients you lost while ill). You mother was just doing what she could to help you get better. Anyone that lets some "pledge" get in the way of their health needs take some serious inventory on what their priorities are.