This is a REALLY good post, and the exact mindset you need right now J.
As far as a specific rehab protocol, I’m sure we can help. First, commit to taking time off loading all exercises. You need some healing.
If inflammation is an issue, 2x400mg IB is not enough. My protocols in the past have been 4x400mg. 1600mg/day.
Start walking. A few miles per day would be good, if you can make the time.
I feel pretty confident that strengthening is the answer vs stretching/mobility, but the right amount of both is the answer.
For the shoulders, begin with 2 x 2 min active hangs. Then perform the super D protocol 2x. Then 3X10 YTWLs.
For the hips, begin with rolling the hip flexors, quads, glute med/max. I like a lacrosse ball for the glutes in fig 4. Next, hit side planks with the top leg abducting, for say 3x10. https://youtu.be/A8VmXRbB8iw
Then work some hollow holds to help with strengthening lower core and reinforce pelvic positioning, 2 x max. You may want to watch a vid and start with a regression. It’s a hard move done correctly. Then work on strengthening your hip flexors, this is a good one: https://youtu.be/7PmC1KG0hc8
You can also play around with Copenhagen side planks. Start with a simple isometric hold. Then you can move into progressions.
I wouldn’t stretch much.
Hope this helps. @FlatsFarmer can add some thoughts I’m sure.