Your issue is therapeutic and there is no asana pill, I’m sorry.
The shoulder joint is a sketchy joint to begin with. Look at it anatomically and there’s almost nothing there - which is why the arm movement is so versatile and amazing.
It would not come as any surprise to me that the rotator cuff muscles (supraspinatus, infraspinatus, teres minor, and supscapularis) may have been strained by Chaturanga. It is far too prevalent in many asana practices and as a result of its frequency it is poorly executed and there is little left of it in the way of bio-mechanical integrity.
That having been said, the issue needs assessment. That can be achieved in several ways - an ortho or physio as they say in the UK or a chiro. You can also go to a therapeutically trained yoga teacher - if you want a more holistic approach to healing.
I suggest Drew Stallcop as he is a certified Purna Yoga teacher (at the 2,000 hour level) there in the UK.