What can cause severe shoulder pain (radiates down towards elbow) and popping with a normal MRI? Also didn't get better with physical therapy.

Popping. As for the popping that is generally just a normal variant. The question on the pain is, is the MRI of the neck or shoulder. IF the shoulder was it done with contrast or without? There are some things like labral tears (if you play sports) that could cause pain. Also, how long have you had the pain. Sometimes there is an injury that is minor and can't be seen but is painful. Give it 6-8 week.