Disclaimer: This is a complete (educated) guess. You must go to see a physio, who lifts weights (night and day to me- non-training physios may know anatomy but not sports injuries too well).
The fall on the elbow, and subsequent clicking and popping sounds to me like an ac joint sprain. I had this in the left shoulder. I did lots of things to help.
Keys:
Don’t sleep on your side, sleep on your back instead. Put your head between two pillows in a little valley to stop you rolling about.
Do lots of scap wall slides, some external rotations.
Light massage of upper trapezius, lats and pec minor may well help.
You may have to do limited ROM shoulder work for a while: e.g. do not lower bar all the way to clavicle on OHP, and do lateral raises from your side, raising only to about 30degrees from parallel to floor. Further than this and you get popping and pain.
Strengthen your lower trapezius/rhomboids, with strict bent over rows where you shrug back and down. This will help offset the pull you likely have which makes your shoulders hurt.
Practice military posture, all the time. Chest up, shoulders down and back (when I cue my girlfriend the prompt is ‘big tits’ if that makes sense lol)
I’ve had chronic shoulder problems in the past, have contributed to lots of threads on the topic, have a look to see if other people (wiser than me) have said anything useful in them maybe? :
I hope that helps mate