Try subscapular release through the armpit. It sounds gross and unpleasant (I guess it is), but it helps me with ring dip/push-up/bench pain. You can use your hand but I prefer something like a broom handle (it works!). Try with your hand first, keeping it close to your rib cage, push into your armpit into the underside of your scapula. It’s a strange sensation but if it’s anything like mine, your shoulders will start to clear up.