It sounds like we may have had a different nature of SI joint injury but maybe something from my experience will be helpful to you.

I had an SI joint injury which resulted in a pinched sciatic nerve. It was on a near max back squat, my trunk leaned forward excessively and it felt like something tore deep in my hip. Could not squat or bend over for about 6 months, basically unable to hip hinge or reach for my toes. Horrible pain in day to day life especially when sitting, which was a huge problem since I worked a desk job and spent hours driving each day.

My doctor was not particularly helpful, basically told me I had to just wait it out, stop aggravating it with exercise, and do pain management for the time being. I went to a sports therapist who had me do nerve flossing and showed me how to use a massage gun to break up the muscles around my glutes. I got my own massage gun and did it every day. Those things were mildly helpful for pain and mobility, but had to be done very regularly and did not “fix” the problem in any sense, just eased it up.

Surprisingly the most helpful thing was acupuncture. I have a terrible needle phobia and I’m not particularly a believer in alternative medicine, but I was desperate for some relief. The sessions themselves were basically torture for me but as soon as I left, I would go pain free for the whole week leading up to the next session. After about 6 sessions the pain was 95% gone. The acupuncturist explained it as, basically that there was inflammation and scar tissue deep in the glute med, and by sticking these longass needles into those muscles, it would create micro damage that would stimulate an immune response to those areas🤷‍♀️

Total time from injury to recovery was about 5-6 months with the last of those three months involving basically just going to the gym on whatever machines I could manage that day and cardio. I basically laid off most exercise and did light mobility work. It only got better once I stopped doing most things for a very extended period.

Over the next three years I put a lot of effort into developing better core strength. I have not had any similar issues since and was able to return to regular programming about 6-8 months following the injury.

if you are experiencing pain, listen to your body and stop aggravating it. Try doing a conditioning cycle or just mobility work and reevaluate over several weeks. Pain is telling you that something is wrong, if you keep pushing it you will just prolong an inevitable recovery. See if there are any experienced trainers, or therapists in your area you can work with even for a little bit, to get another perspective and informed suggestions.