I'd cut the shrugs and the lat raises for a while. You may need to limit some of your exercises and really focus on strengthening your posterior capsule. Alot of times but not always, injuries like this can be caused from anterior tightness which leads to posterior instability. Working on your daily postrue may help also, sitting up right in chairs, shoulders down and back.
Same thing when standing or walking... dont have to walk around looking like you're trying to start a fight, but practicing good posture can stimulate those muscles into firing properly again. I switched from sleeping with 2 pillows under my head to sleeping with no pillows. The rational was the overnight flexion in my neck was aggravating my neck and back.
Machine variations of pressing and db's were easier for me. DB's for OHP, real light at first, incline, also light, couldn't bench so i did push ups, set of 3 before my shoulder gave out, curls, pully triceps pushdown, eased into machine bench, chin grip for pulldowns on the machine were all i could do but eventually worked in overhand grip and worked in real chins and eventually pull ups.
But i really focused on anything that had me squeezing my shoulder blades "down and back". daily stretching of your pec and biceps paired with strengthening rear delts, rhomboids, lower traps and lats. Shrugs gave me alot of problems so i cut them until i felt 100%. something like Waterbury's "bodybuilding's next frontier" program could really be helpful. Frequency and controlling fatigue helped me alot, didn't push it on every workout but pushed for benchmark achievements. I did 20lb db's for 6 and got kinda tight last time, try to get a solid 6 this time or 25 for an acceptable 6.
But if you can't do full movements, do partials. And strive for improvement there or strive for working progressively towards a full ROM. Keep a log, and if after a month or so you haven't experienced any gains in strength/stability I'd get an MRI on your neck or thoracic spine to check for any nerve damage stemming from the vertebrae. I know it's frustrating but the body is pretty good at repairing itself, it's just about finding what your body is preventing your body from getting back on track. Keep us posted.