By the way if pulse goes away when you pinch shoulder blades back this tells me ( once again I'm not a doctor ) that you have pec minor involvement. Why? Because the pic minor actually inserts into the caracoid process which is actually part of the scapula. When you pull them back it actually is tightening that bit of muscle in the front of your chest like a fish fighting you on a fishing line...

This is why I say have some soft tissue work done on your pec. Dry needling the pec minor has been amazing for me. A lot of people with pec minor syndrome also find that their shoulders are unstable and they have some winging of the scapula. Find an expert PT that is able to help stabilize your shoulder joint but also has techniques to loosen up that pic minor. I might guess you have tight traps too, maybe some pain in the scapula area, difficulty turning neck to the painful side?