How To Treat Discomfort In Arm Movement Caused Due To An Injury?

My husband is having difficulty lifting his left arm straight up. He took a fall at work and heard something pop. He has been going to the chiropractor who thinks it is getting better. It doesn't hurt but he just can't raise it. He can move the arm forward and it bends fine at the elbow but he can't bring it up. Should he have an MRI done on it to see if he damaged something badly?