Broken collar bone hurts?

Yep, I bet it does. Most heal without surgery without resulting in significant residual pain and/or dysfunction. If the doctor is concerned that it won't heal without surgery or that it would heal and result in pain and/or dysfunction, the doctor will discuss surgery. Those that require surgery usually do great after surgery.
Be seen. Would want to be seen and evaluated. Ice, sling, and medication can all help reduce pain from a broken collarbone.