I went through your statement. You have GERD
and your suspicion of upper respiratory part - both may not be connected with your present problem.
You are getting your problem only while dong treadmill test. So more in favor of muscle pain
You are able to move your both arms front and back - So arthritis
can also be ruled out.
Better to take an X-Ray chest including both shoulder joints.
if no problems in the bones you can take it for granted that it is only a muscle pain. Find out which part of the muscle is paining by movement and pressure and take pain killers + anti inflammatory cream local application.
You will be alright. Anyhow it is better to take ECG. Give rest to muscles by avoiding Treadmill for certain days.