Although my injury was different, my doc gave a similar diagnosis & plan of action. I looked at him & asked "Based on your experience, are the chances high that after PT, I'm going to be back here with the same issue & getting the MRI? If so, lets skip that part & get the MRI now". I got the MRI. It showed a torn rotator cuff tendon. Had surgery (where he severed damaged tendon & reattached it) - then post-surgery PT.
My shoulder is now fine but do not underestimate the amount of lost biking time, hours spent in PT (both with physical therapist & at home) & high levels of pain.