I have a messed up SI joint and some arthritis and bulging disks in the general area. I also have a problematic piriformis.The shooting pain down your leg is a very annoyed sciatic nerve.
I also spend far too long sitting at my desk at a stretch.
I’m much older that you, so I have injections in my SI and Piriformis about once a year to get it to shut up and leave me alone. They generally work pretty well, but I’d be a bit worried about doing them at your age unless you are in agony.
Be very careful about chairs, car seats and, a biggie, saddle fit.
(I have been miserably uncomfortable recently. My horse has been off work for 6 months and I am just starting him back under saddle. He’s lost a lot of top line and as a result my saddle was unlevel and I was fighting for my position. And all we have been doing is walking, which isn’t the best motion for my lower back. So I had my saddle refitted on Wednesday. Since then, I’ve slept through the night. Just a little tweak, but night and day difference.)
I also hand walk for at least 5 minutes before I get on, and 5 minutes after I get off, just to get everything moving.