Are you addressing the lack of elbow flexion in that arm?
Have you addressed areas up stream and down stream of where you are seeing the issue?
Yes, working with your neck can free up things in your shoulder. Keep working with this.
If you aren’t seeing improvements with what you are addressing your are not hitting the cause of the issue yet. If your first rib is out that can cause other things not to have proper positioning which are contributing factors to what you are experiencing.