It is my understanding that the only way to know for sure that an arm is not broken is to take an X-ray and then get it read correctly. (Getting X-ray's read correctly is a crapshoot.)
We do not do that every time we bang are arms because there are ways to know for almost sure. A doctor has done those things to me and concluded that an X-ray shouldn't be necessary because my arm is for almost sure not broken.
So: yay! In theory my arm should be better in a week to ten days. Also I've learned additional diagnostic tests to check if an arm is broken that they didn't teach in wilderness first aid or lifeguard certification.